{"uri":"http://uri.gbv.de/terminology/msc2020/00-XX","notation":["00-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General and overarching topics; collections"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00-01","notation":["00-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00-XX","notation":["00-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00-02","notation":["00-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to mathematics in general"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00-XX","notation":["00-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General and miscellaneous specific topics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00-XX","notation":["00-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A05","notation":["00A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematics in general"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A06","notation":["00A06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematics for nonmathematicians (engineering, social sciences, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A07","notation":["00A07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Problem books"},"scopeNote":{"en":["For open problems, see 00A27"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A08","notation":["00A08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Recreational mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A09","notation":["00A09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Popularization of mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A15","notation":["00A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bibliographies for mathematics in general"},"scopeNote":{"en":["See also 01A70 and the classification number –00 in the other sections"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A17","notation":["00A17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"External book reviews"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A20","notation":["00A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dictionaries and other general reference works"},"scopeNote":{"en":["See also the classification number –00 in the other sections"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A22","notation":["00A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Formularies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A27","notation":["00A27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lists of open problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A30","notation":["00A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Philosophy of mathematics"},"scopeNote":{"en":["See also 03A05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A35","notation":["00A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methodology of mathematics"},"scopeNote":{"en":["For mathematics education, see 97-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A64","notation":["00A64"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematics and literature"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A65","notation":["00A65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematics and music"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A66","notation":["00A66"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematics and visual arts"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A67","notation":["00A67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematics and architecture"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A69","notation":["00A69"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General applied mathematics"},"scopeNote":{"en":["For physics, see 00A79 and Sections 70 through 86"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A71","notation":["00A71"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of mathematical modeling"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A72","notation":["00A72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of simulation"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A79","notation":["00A79"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Physics (Use more specific entries from Sections 70 through 86 when possible)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00A99","notation":["00A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Axx","notation":["00Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00Bxx","notation":["00Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Conference proceedings and collections of articles"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00-XX","notation":["00-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00B05","notation":["00B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Collections of abstracts of lectures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Bxx","notation":["00Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00B10","notation":["00B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Collections of articles of general interest"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Bxx","notation":["00Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00B15","notation":["00B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Collections of articles of miscellaneous specific interest"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Bxx","notation":["00Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00B20","notation":["00B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings of conferences of general interest"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Bxx","notation":["00Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00B25","notation":["00B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings of conferences of miscellaneous specific interest"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Bxx","notation":["00Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00B30","notation":["00B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Festschriften"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Bxx","notation":["00Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00B50","notation":["00B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Collections of translated articles of general interest"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Bxx","notation":["00Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00B55","notation":["00B55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Collections of translated articles of miscellaneous specific interest"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Bxx","notation":["00Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00B60","notation":["00B60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Collections of reprinted articles"},"scopeNote":{"en":["See also 01A75"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Bxx","notation":["00Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/00B99","notation":["00B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/00Bxx","notation":["00Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01-XX","notation":["01-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History and biography"},"scopeNote":{"en":["See also the classification number –03 in the other sections"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01-00","notation":["01-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to history and biography"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01-XX","notation":["01-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01-01","notation":["01-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to history and biography"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01-XX","notation":["01-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01-02","notation":["01-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to history and biography"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01-XX","notation":["01-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01-06","notation":["01-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to history and biography"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01-XX","notation":["01-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01-11","notation":["01-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to history and biography"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01-XX","notation":["01-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics and mathematicians"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01-XX","notation":["01-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A05","notation":["01A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General histories, source books"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A07","notation":["01A07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ethnomathematics, general"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A10","notation":["01A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in Paleolithic and Neolithic times"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A11","notation":["01A11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics of the indigenous cultures of Africa, Asia, and Oceania"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A12","notation":["01A12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics of the indigenous cultures of the Americas"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A15","notation":["01A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics of the indigenous cultures of Europe (pre-Greek, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A16","notation":["01A16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in Ancient Egypt"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A17","notation":["01A17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in Ancient Babylon"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A20","notation":["01A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in Ancient Greece and Rome"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A25","notation":["01A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in China"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A27","notation":["01A27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in Japan"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A29","notation":["01A29"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in Southeast Asia"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A30","notation":["01A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in the Golden Age of Islam"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A32","notation":["01A32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in India"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A35","notation":["01A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in late antiquity and medieval Europe"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A40","notation":["01A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in the 15th and 16th centuries, Renaissance"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A45","notation":["01A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in the 17th century"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A50","notation":["01A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in the 18th century"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A55","notation":["01A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in the 19th century"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A60","notation":["01A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in the 20th century"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A61","notation":["01A61"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics in the 21st century"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A65","notation":["01A65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Development of contemporary mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A67","notation":["01A67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Future perspectives in mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A70","notation":["01A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biographies, obituaries, personalia, bibliographies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A72","notation":["01A72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Schools of mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A73","notation":["01A73"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics at specific universities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A74","notation":["01A74"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics at institutions and academies (non-university)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A75","notation":["01A75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Collected or selected works; reprintings or translations of classics"},"scopeNote":{"en":["See also 00B60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A80","notation":["01A80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sociology (and profession) of mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A85","notation":["01A85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Historiography"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A90","notation":["01A90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bibliographic studies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/01A99","notation":["01A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/01Axx","notation":["01Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical logic and foundations"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03-00","notation":["03-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematical logic and foundations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03-01","notation":["03-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03-02","notation":["03-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03-03","notation":["03-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematical logic and foundations"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03-04","notation":["03-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to mathematical logic and foundations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03-06","notation":["03-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03-08","notation":["03-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to mathematical logic and foundations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03-11","notation":["03-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to mathematical logic and foundations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03Axx","notation":["03Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Philosophical aspects of logic and foundations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03A05","notation":["03A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Philosophical and critical aspects of logic and foundations"},"scopeNote":{"en":["For philosophy of mathematics, see also 00A30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Axx","notation":["03Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03A10","notation":["03A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logic in the philosophy of science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Axx","notation":["03Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03A99","notation":["03A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Axx","notation":["03Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B05","notation":["03B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical propositional logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B10","notation":["03B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical first-order logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B16","notation":["03B16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-order logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B20","notation":["03B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subsystems of classical logic (including intuitionistic logic)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B22","notation":["03B22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract deductive systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B25","notation":["03B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Decidability of theories and sets of sentences"},"scopeNote":{"en":["See also 11U05, 12L05, 20F10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B30","notation":["03B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations of classical theories (including reverse mathematics)"},"scopeNote":{"en":["See also 03F35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B35","notation":["03B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mechanization of proofs and logical operations"},"scopeNote":{"en":["See also 68V15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B38","notation":["03B38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Type theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B40","notation":["03B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatory logic and lambda calculus"},"scopeNote":{"en":["See also 68N18"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B42","notation":["03B42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logics of knowledge and belief (including belief change)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B44","notation":["03B44"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Temporal logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B45","notation":["03B45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modal logic (including the logic of norms)"},"scopeNote":{"en":["For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B47","notation":["03B47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)"},"scopeNote":{"en":["For proof-theoretic aspects see 03F52"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B48","notation":["03B48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probability and inductive logic"},"scopeNote":{"en":["See also 60A05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B50","notation":["03B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Many-valued logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B52","notation":["03B52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy logic; logic of vagueness"},"scopeNote":{"en":["See also 68T27, 68T37, 94D05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B53","notation":["03B53"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Paraconsistent logics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B55","notation":["03B55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Intermediate logics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B60","notation":["03B60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other nonclassical logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B62","notation":["03B62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combined logics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B65","notation":["03B65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logic of natural languages"},"scopeNote":{"en":["See also 68T50, 91F20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B70","notation":["03B70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logic in computer science"},"scopeNote":{"en":["See also 68-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B80","notation":["03B80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other applications of logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03B99","notation":["03B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Bxx","notation":["03Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Model theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C05","notation":["03C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equational classes, universal algebra in model theory"},"scopeNote":{"en":["See also 08Axx, 08Bxx, 18C05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C07","notation":["03C07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Basic properties of first-order languages and structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C10","notation":["03C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantifier elimination, model completeness and related topics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C13","notation":["03C13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Model theory of finite structures"},"scopeNote":{"en":["See also 68Q15, 68Q19"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C15","notation":["03C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Model theory of denumerable and separable structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C20","notation":["03C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ultraproducts and related constructions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C25","notation":["03C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Model-theoretic forcing"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C30","notation":["03C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other model constructions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C35","notation":["03C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categoricity and completeness of theories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C40","notation":["03C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Interpolation, preservation, definability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C45","notation":["03C45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classification theory, stability and related concepts in model theory"},"scopeNote":{"en":["See also 03C48"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C48","notation":["03C48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract elementary classes and related topics"},"scopeNote":{"en":["See also 03C45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C50","notation":["03C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Models with special properties (saturated, rigid, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C52","notation":["03C52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Properties of classes of models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C55","notation":["03C55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set-theoretic model theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C57","notation":["03C57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computable structure theory, computable model theory"},"scopeNote":{"en":["See also 03D45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C60","notation":["03C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Model-theoretic algebra"},"scopeNote":{"en":["See also 08C10, 12Lxx, 13L05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C62","notation":["03C62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Models of arithmetic and set theory"},"scopeNote":{"en":["See also 03Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C64","notation":["03C64"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Model theory of ordered structures; o-minimality"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C65","notation":["03C65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Models of other mathematical theories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C66","notation":["03C66"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuous model theory, model theory of metric structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C68","notation":["03C68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other classical first-order model theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C70","notation":["03C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logic on admissible sets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C75","notation":["03C75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other infinitary logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C80","notation":["03C80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logic with extra quantifiers and operators"},"scopeNote":{"en":["See also 03B42, 03B44, 03B45, 03B48"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C85","notation":["03C85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Second- and higher-order model theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C90","notation":["03C90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonclassical models (Boolean-valued, sheaf, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C95","notation":["03C95"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract model theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C98","notation":["03C98"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of model theory"},"scopeNote":{"en":["See also 03C60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03C99","notation":["03C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Cxx","notation":["03Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computability and recursion theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D03","notation":["03D03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Thue and Post systems, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D05","notation":["03D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automata and formal grammars in connection with logical questions"},"scopeNote":{"en":["See also 68Q45, 68Q70, 68R15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D10","notation":["03D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Turing machines and related notions"},"scopeNote":{"en":["See also 68Q04"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D15","notation":["03D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complexity of computation (including implicit computational complexity)"},"scopeNote":{"en":["See also 68Q15, 68Q17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D20","notation":["03D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Recursive functions and relations, subrecursive hierarchies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D25","notation":["03D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Recursively (computably) enumerable sets and degrees"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D28","notation":["03D28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other Turing degree structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D30","notation":["03D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other degrees and reducibilities in computability and recursion theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D32","notation":["03D32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algorithmic randomness and dimension"},"scopeNote":{"en":["See also 68Q30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D35","notation":["03D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Undecidability and degrees of sets of sentences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D40","notation":["03D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Word problems, etc. in computability and recursion theory"},"scopeNote":{"en":["See also 06B25, 08A50, 20F10, 68R15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D45","notation":["03D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of numerations, effectively presented structures"},"scopeNote":{"en":["See also 03C57; For intuitionistic and similar approaches, see 03F55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D50","notation":["03D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Recursive equivalence types of sets and structures, isols"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D55","notation":["03D55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hierarchies of computability and definability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D60","notation":["03D60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computability and recursion theory on ordinals, admissible sets, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D65","notation":["03D65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-type and set recursion theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D70","notation":["03D70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inductive definability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D75","notation":["03D75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract and axiomatic computability and recursion theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D78","notation":["03D78"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computation over the reals, computable analysis"},"scopeNote":{"en":["For constructive aspects, see 03F60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D80","notation":["03D80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of computability and recursion theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03D99","notation":["03D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Dxx","notation":["03Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E02","notation":["03E02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partition relations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E04","notation":["03E04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered sets and their cofinalities; pcf theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E05","notation":["03E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other combinatorial set theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E10","notation":["03E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinal and cardinal numbers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E15","notation":["03E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Descriptive set theory"},"scopeNote":{"en":["See also 28A05, 54H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E17","notation":["03E17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cardinal characteristics of the continuum"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E20","notation":["03E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other classical set theory (including functions, relations, and set algebra)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E25","notation":["03E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axiom of choice and related propositions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E30","notation":["03E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axiomatics of classical set theory and its fragments"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E35","notation":["03E35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Consistency and independence results"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E40","notation":["03E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other aspects of forcing and Boolean-valued models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E45","notation":["03E45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inner models, including constructibility, ordinal definability, and core models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E47","notation":["03E47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other notions of set-theoretic definability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E50","notation":["03E50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuum hypothesis and Martin’s axiom"},"scopeNote":{"en":["See also 03E57"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E55","notation":["03E55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Large cardinals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E57","notation":["03E57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generic absoluteness and forcing axioms"},"scopeNote":{"en":["See also 03E50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E60","notation":["03E60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Determinacy principles"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E65","notation":["03E65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other set-theoretic hypotheses and axioms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E70","notation":["03E70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonclassical and second-order set theories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E72","notation":["03E72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of fuzzy sets, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E75","notation":["03E75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of set theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03E99","notation":["03E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Exx","notation":["03Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proof theory and constructive mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F03","notation":["03F03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proof theory, general (including proof-theoretic semantics)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F05","notation":["03F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cut-elimination and normal-form theorems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F07","notation":["03F07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure of proofs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F10","notation":["03F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functionals in proof theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F15","notation":["03F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Recursive ordinals and ordinal notations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F20","notation":["03F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complexity of proofs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F25","notation":["03F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relative consistency and interpretations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F30","notation":["03F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"First-order arithmetic and fragments"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F35","notation":["03F35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Second- and higher-order arithmetic and fragments"},"scopeNote":{"en":["See also 03B30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F40","notation":["03F40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gödel numberings and issues of incompleteness"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F45","notation":["03F45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Provability logics and related algebras (e.g., diagonalizable algebras)"},"scopeNote":{"en":["See also 03B45, 03G25, 06E25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F50","notation":["03F50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Metamathematics of constructive systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F52","notation":["03F52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proof-theoretic aspects of linear logic and other substructural logics"},"scopeNote":{"en":["See also 03B47"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F55","notation":["03F55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Intuitionistic mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F60","notation":["03F60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Constructive and recursive analysis"},"scopeNote":{"en":["See also 03B30, 03D45, 03D78, 26E40, 46S30, 47S30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F65","notation":["03F65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other constructive mathematics"},"scopeNote":{"en":["See also 03D45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03F99","notation":["03F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Fxx","notation":["03Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03Gxx","notation":["03Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03G05","notation":["03G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logical aspects of Boolean algebras"},"scopeNote":{"en":["See also 06Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Gxx","notation":["03Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03G10","notation":["03G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logical aspects of lattices and related structures"},"scopeNote":{"en":["See also 06Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Gxx","notation":["03Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03G12","notation":["03G12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum logic"},"scopeNote":{"en":["See also 06C15, 81P10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Gxx","notation":["03Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03G15","notation":["03G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cylindric and polyadic algebras; relation algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Gxx","notation":["03Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03G20","notation":["03G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logical aspects of Lukasiewicz and Post algebras"},"scopeNote":{"en":["See also 06D25, 06D30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Gxx","notation":["03Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03G25","notation":["03G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other algebras related to logic"},"scopeNote":{"en":["See also 03F45, 06D20, 06E25, 06F35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Gxx","notation":["03Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03G27","notation":["03G27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract algebraic logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Gxx","notation":["03Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03G30","notation":["03G30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categorical logic, topoi"},"scopeNote":{"en":["See also 18B25, 18C05, 18C10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Gxx","notation":["03Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03G99","notation":["03G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Gxx","notation":["03Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03Hxx","notation":["03Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonstandard models"},"scopeNote":{"en":["See also 03C62"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03-XX","notation":["03-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03H05","notation":["03H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonstandard models in mathematics"},"scopeNote":{"en":["See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Hxx","notation":["03Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03H10","notation":["03H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other applications of nonstandard models (economics, physics, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Hxx","notation":["03Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03H15","notation":["03H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonstandard models of arithmetic"},"scopeNote":{"en":["See also 11U10, 12L15, 13L05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Hxx","notation":["03Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/03H99","notation":["03H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/03Hxx","notation":["03Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorics"},"scopeNote":{"en":["For finite fields, see 11Txx"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05-00","notation":["05-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to combinatorics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05-01","notation":["05-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05-02","notation":["05-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to combinatorics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05-03","notation":["05-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of combinatorics"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05-04","notation":["05-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to combinatorics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05-06","notation":["05-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to combinatorics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05-08","notation":["05-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to combinatorics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05-11","notation":["05-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to combinatorics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05Axx","notation":["05Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Enumerative combinatorics"},"scopeNote":{"en":["For enumeration in graph theory, see 05C30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05A05","notation":["05A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Permutations, words, matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Axx","notation":["05Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05A10","notation":["05A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Factorials, binomial coefficients, combinatorial functions"},"scopeNote":{"en":["See also 11B65, 33Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Axx","notation":["05Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05A15","notation":["05A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exact enumeration problems, generating functions"},"scopeNote":{"en":["See also 33Cxx, 33Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Axx","notation":["05Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05A16","notation":["05A16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic enumeration"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Axx","notation":["05Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05A17","notation":["05A17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of partitions of integers"},"scopeNote":{"en":["See also 11P81, 11P82, 11P83"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Axx","notation":["05Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05A18","notation":["05A18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partitions of sets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Axx","notation":["05Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05A19","notation":["05A19"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial identities, bijective combinatorics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Axx","notation":["05Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05A20","notation":["05A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial inequalities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Axx","notation":["05Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05A30","notation":["05A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"q-calculus and related topics"},"scopeNote":{"en":["See also 33Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Axx","notation":["05Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05A40","notation":["05A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Umbral calculus"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Axx","notation":["05Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05A99","notation":["05A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Axx","notation":["05Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Designs and configurations"},"scopeNote":{"en":["For applications of design theory, see 94C30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05B05","notation":["05B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of block designs"},"scopeNote":{"en":["See also 51E05, 62K10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05B07","notation":["05B07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Triple systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05B10","notation":["05B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)"},"scopeNote":{"en":["See also 11B13"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05B15","notation":["05B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orthogonal arrays, Latin squares, Room squares"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05B20","notation":["05B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of matrices (incidence, Hadamard, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05B25","notation":["05B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of finite geometries"},"scopeNote":{"en":["See also 51D20, 51Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05B30","notation":["05B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other designs, configurations"},"scopeNote":{"en":["See also 51E30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05B35","notation":["05B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of matroids and geometric lattices"},"scopeNote":{"en":["See also 52B40, 90C27"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05B40","notation":["05B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of packing and covering"},"scopeNote":{"en":["See also 11H31, 52C15, 52C17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05B45","notation":["05B45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of tessellation and tiling problems"},"scopeNote":{"en":["See also 52C20, 52C22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05B50","notation":["05B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polyominoes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05B99","notation":["05B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Bxx","notation":["05Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graph theory"},"scopeNote":{"en":["For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C05","notation":["05C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Trees"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C07","notation":["05C07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vertex degrees"},"scopeNote":{"en":["See also 05E30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C09","notation":["05C09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graphical indices (Wiener index, Zagreb index, Randić index, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C10","notation":["05C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Planar graphs; geometric and topological aspects of graph theory"},"scopeNote":{"en":["See also 57K10, 57M15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C12","notation":["05C12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distance in graphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C15","notation":["05C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Coloring of graphs and hypergraphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C17","notation":["05C17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perfect graphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C20","notation":["05C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Directed graphs (digraphs), tournaments"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C21","notation":["05C21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Flows in graphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C22","notation":["05C22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Signed and weighted graphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C25","notation":["05C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graphs and abstract algebra (groups, rings, fields, etc.)"},"scopeNote":{"en":["See also 20F65"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C30","notation":["05C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Enumeration in graph theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C31","notation":["05C31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graph polynomials"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C35","notation":["05C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extremal problems in graph theory"},"scopeNote":{"en":["See also 90C35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C38","notation":["05C38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Paths and cycles"},"scopeNote":{"en":["See also 90B10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C40","notation":["05C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connectivity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C42","notation":["05C42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Density (toughness, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C45","notation":["05C45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Eulerian and Hamiltonian graphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C48","notation":["05C48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Expander graphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C50","notation":["05C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graphs and linear algebra (matrices, eigenvalues, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C51","notation":["05C51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graph designs and isomorphic decomposition"},"scopeNote":{"en":["See also 05B30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C55","notation":["05C55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized Ramsey theory"},"scopeNote":{"en":["See also 05D10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C57","notation":["05C57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Games on graphs (graph-theoretic aspects)"},"scopeNote":{"en":["See also 91A43, 91A46"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C60","notation":["05C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C62","notation":["05C62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graph representations (geometric and intersection representations, etc.)"},"scopeNote":{"en":["For graph drawing, see also 68R10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C63","notation":["05C63"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite graphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C65","notation":["05C65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hypergraphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C69","notation":["05C69"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C70","notation":["05C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C72","notation":["05C72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fractional graph theory, fuzzy graph theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C75","notation":["05C75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structural characterization of families of graphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C76","notation":["05C76"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graph operations (line graphs, products, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C78","notation":["05C78"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graph labelling (graceful graphs, bandwidth, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C80","notation":["05C80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random graphs (graph-theoretic aspects)"},"scopeNote":{"en":["See also 60B20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C81","notation":["05C81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random walks on graphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C82","notation":["05C82"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Small world graphs, complex networks (graph-theoretic aspects)"},"scopeNote":{"en":["See also 90Bxx, 91D30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C83","notation":["05C83"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graph minors"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C85","notation":["05C85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graph algorithms (graph-theoretic aspects)"},"scopeNote":{"en":["See also 68R10, 68W05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C90","notation":["05C90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of graph theory"},"scopeNote":{"en":["See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C92","notation":["05C92"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chemical graph theory"},"scopeNote":{"en":["See also 92E10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05C99","notation":["05C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Cxx","notation":["05Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05Dxx","notation":["05Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extremal combinatorics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05D05","notation":["05D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extremal set theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Dxx","notation":["05Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05D10","notation":["05D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ramsey theory"},"scopeNote":{"en":["See also 05C55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Dxx","notation":["05Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05D15","notation":["05D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transversal (matching) theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Dxx","notation":["05Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05D40","notation":["05D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Dxx","notation":["05Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05D99","notation":["05D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Dxx","notation":["05Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05Exx","notation":["05Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic combinatorics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05-XX","notation":["05-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05E05","notation":["05E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symmetric functions and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Exx","notation":["05Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05E10","notation":["05E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of representation theory"},"scopeNote":{"en":["See also 20C30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Exx","notation":["05Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05E14","notation":["05E14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of algebraic geometry"},"scopeNote":{"en":["See also 14Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Exx","notation":["05Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05E16","notation":["05E16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of groups and algebras"},"scopeNote":{"en":["See also 22E45, 33C80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Exx","notation":["05Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05E18","notation":["05E18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group actions on combinatorial structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Exx","notation":["05Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05E30","notation":["05E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Association schemes, strongly regular graphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Exx","notation":["05Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05E40","notation":["05E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of commutative algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Exx","notation":["05Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05E45","notation":["05E45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of simplicial complexes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Exx","notation":["05Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/05E99","notation":["05E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/05Exx","notation":["05Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Order, lattices, ordered algebraic structures"},"scopeNote":{"en":["See also 18B35"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06-00","notation":["06-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordered structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06-01","notation":["06-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordered structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06-02","notation":["06-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to ordered structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06-03","notation":["06-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of ordered structures"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06-04","notation":["06-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to ordered structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06-06","notation":["06-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to ordered structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06-08","notation":["06-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to ordered structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06-11","notation":["06-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to ordered structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06Axx","notation":["06Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered sets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06A05","notation":["06A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Total orders"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Axx","notation":["06Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06A06","notation":["06A06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partial orders, general"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Axx","notation":["06Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06A07","notation":["06A07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorics of partially ordered sets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Axx","notation":["06Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06A11","notation":["06A11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic aspects of posets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Axx","notation":["06Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06A12","notation":["06A12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semilattices"},"scopeNote":{"en":["See also 20M10; For topological semilattices, see 22A26"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Axx","notation":["06Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06A15","notation":["06A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Galois correspondences, closure operators (in relation to ordered sets)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Axx","notation":["06Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06A75","notation":["06A75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of ordered sets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Axx","notation":["06Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06A99","notation":["06A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Axx","notation":["06Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06Bxx","notation":["06Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattices"},"scopeNote":{"en":["See also 03G10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06B05","notation":["06B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure theory of lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Bxx","notation":["06Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06B10","notation":["06B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattice ideals, congruence relations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Bxx","notation":["06Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06B15","notation":["06B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representation theory of lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Bxx","notation":["06Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06B20","notation":["06B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Varieties of lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Bxx","notation":["06Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06B23","notation":["06B23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complete lattices, completions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Bxx","notation":["06Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06B25","notation":["06B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free lattices, projective lattices, word problems"},"scopeNote":{"en":["See also 03D40, 08A50, 20F10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Bxx","notation":["06Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06B30","notation":["06B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological lattices"},"scopeNote":{"en":["See also 06F30, 22A26, 54F05, 54H12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Bxx","notation":["06Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06B35","notation":["06B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuous lattices and posets, applications"},"scopeNote":{"en":["See also 06B30, 06D10, 06F30, 18B35, 22A26, 68Q55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Bxx","notation":["06Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06B75","notation":["06B75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Bxx","notation":["06Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06B99","notation":["06B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Bxx","notation":["06Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06Cxx","notation":["06Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modular lattices, complemented lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06C05","notation":["06C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modular lattices, Desarguesian lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Cxx","notation":["06Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06C10","notation":["06C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semimodular lattices, geometric lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Cxx","notation":["06Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06C15","notation":["06C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complemented lattices, orthocomplemented lattices and posets"},"scopeNote":{"en":["See also 03G12, 81P10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Cxx","notation":["06Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06C20","notation":["06C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complemented modular lattices, continuous geometries"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Cxx","notation":["06Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06C99","notation":["06C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Cxx","notation":["06Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06Dxx","notation":["06Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distributive lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06D05","notation":["06D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure and representation theory of distributive lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Dxx","notation":["06Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06D10","notation":["06D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complete distributivity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Dxx","notation":["06Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06D15","notation":["06D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pseudocomplemented lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Dxx","notation":["06Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06D20","notation":["06D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Heyting algebras (lattice-theoretic aspects)"},"scopeNote":{"en":["See also 03G25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Dxx","notation":["06Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06D22","notation":["06D22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Frames, locales"},"scopeNote":{"en":["For topological questions, see 54-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Dxx","notation":["06Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06D25","notation":["06D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Post algebras (lattice-theoretic aspects)"},"scopeNote":{"en":["See also 03G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Dxx","notation":["06Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06D30","notation":["06D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"De Morgan algebras, Lukasiewicz algebras (lattice-theoretic aspects)"},"scopeNote":{"en":["See also 03G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Dxx","notation":["06Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06D35","notation":["06D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"MV-algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Dxx","notation":["06Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06D50","notation":["06D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattices and duality"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Dxx","notation":["06Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06D72","notation":["06D72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy lattices (soft algebras) and related topics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Dxx","notation":["06Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06D75","notation":["06D75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other generalizations of distributive lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Dxx","notation":["06Dxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/06Exx","notation":["06Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boolean algebras (Boolean rings)"},"scopeNote":{"en":["See also 03G05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06E05","notation":["06E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure theory of Boolean algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Exx","notation":["06Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06E10","notation":["06E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chain conditions, complete algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Exx","notation":["06Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06E15","notation":["06E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stone spaces (Boolean spaces) and related structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Exx","notation":["06Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06E20","notation":["06E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ring-theoretic properties of Boolean algebras"},"scopeNote":{"en":["See also 16E50, 16G30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Exx","notation":["06Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06E25","notation":["06E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boolean algebras with additional operations (diagonalizable algebras, etc.)"},"scopeNote":{"en":["See also 03G25, 03F45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Exx","notation":["06Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06E30","notation":["06E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boolean functions"},"scopeNote":{"en":["See also 94D10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Exx","notation":["06Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06E75","notation":["06E75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of Boolean algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Exx","notation":["06Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06E99","notation":["06E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Exx","notation":["06Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06Fxx","notation":["06Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06-XX","notation":["06-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06F05","notation":["06F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered semigroups and monoids"},"scopeNote":{"en":["See also 20Mxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Fxx","notation":["06Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06F07","notation":["06F07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantales"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Fxx","notation":["06Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06F10","notation":["06F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noether lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Fxx","notation":["06Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06F15","notation":["06F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered groups"},"scopeNote":{"en":["See also 20F60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Fxx","notation":["06Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06F20","notation":["06F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered abelian groups, Riesz groups, ordered linear spaces"},"scopeNote":{"en":["See also 46A40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Fxx","notation":["06Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06F25","notation":["06F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered rings, algebras, modules"},"scopeNote":{"en":["For ordered fields, see 12J15; See also 13J25, 16W80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Fxx","notation":["06Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06F30","notation":["06F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered topological structures (aspects of ordered structures)"},"scopeNote":{"en":["See also 06B30, 22A26, 54F05, 54H12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Fxx","notation":["06Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06F35","notation":["06F35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"BCK-algebras, BCI-algebras (aspects of ordered structures)"},"scopeNote":{"en":["See also 03G25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Fxx","notation":["06Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/06F99","notation":["06F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/06Fxx","notation":["06Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08-XX","notation":["08-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General algebraic systems"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/08-01","notation":["08-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general algebraic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08-XX","notation":["08-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08-02","notation":["08-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to general algebraic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08-XX","notation":["08-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08-03","notation":["08-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of general algebraic systems"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08-XX","notation":["08-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08-04","notation":["08-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to general algebraic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08-XX","notation":["08-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08-06","notation":["08-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to general algebraic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08-XX","notation":["08-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08-08","notation":["08-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to general algebraic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08-XX","notation":["08-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08-11","notation":["08-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to general algebraic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08-XX","notation":["08-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic structures"},"scopeNote":{"en":["See also 03C05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08-XX","notation":["08-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A02","notation":["08A02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relational systems, laws of composition"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A05","notation":["08A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure theory of algebraic structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A30","notation":["08A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subalgebras, congruence relations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A35","notation":["08A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphisms and endomorphisms of algebraic structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A40","notation":["08A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operations and polynomials in algebraic structures, primal algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A45","notation":["08A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equational compactness"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A50","notation":["08A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Word problems (aspects of algebraic structures)"},"scopeNote":{"en":["See also 03D40, 06B25, 20F10, 68R15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A55","notation":["08A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partial algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A60","notation":["08A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unary algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A62","notation":["08A62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finitary algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A65","notation":["08A65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinitary algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A68","notation":["08A68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Heterogeneous algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A70","notation":["08A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of universal algebra in computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A72","notation":["08A72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy algebraic structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08A99","notation":["08A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Axx","notation":["08Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08Bxx","notation":["08Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Varieties"},"scopeNote":{"en":["See also 03C05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08-XX","notation":["08-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08B05","notation":["08B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equational logic, Mal’tsev conditions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Bxx","notation":["08Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08B10","notation":["08B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Congruence modularity, congruence distributivity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Bxx","notation":["08Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08B15","notation":["08B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattices of varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Bxx","notation":["08Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08B20","notation":["08B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Bxx","notation":["08Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08B25","notation":["08B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Products, amalgamated products, and other kinds of limits and colimits"},"scopeNote":{"en":["See also 18A30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Bxx","notation":["08Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08B26","notation":["08B26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subdirect products and subdirect irreducibility"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Bxx","notation":["08Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08B30","notation":["08B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Injectives, projectives"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Bxx","notation":["08Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08B99","notation":["08B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Bxx","notation":["08Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08Cxx","notation":["08Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other classes of algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08-XX","notation":["08-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08C05","notation":["08C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categories of algebras"},"scopeNote":{"en":["See also 18C05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Cxx","notation":["08Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08C10","notation":["08C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axiomatic model classes"},"scopeNote":{"en":["See also 03Cxx, in particular 03C60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Cxx","notation":["08Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08C15","notation":["08C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasivarieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Cxx","notation":["08Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08C20","notation":["08C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Natural dualities for classes of algebras"},"scopeNote":{"en":["See also 06E15, 18A40, 22A30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Cxx","notation":["08Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/08C99","notation":["08C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/08Cxx","notation":["08Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Number theory"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/11-01","notation":["11-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11-02","notation":["11-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to number theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11-03","notation":["11-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of number theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11-04","notation":["11-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to number theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11-06","notation":["11-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to number theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11-11","notation":["11-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to number theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Axx","notation":["11Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elementary number theory"},"scopeNote":{"en":["For analogues in number fields, see 11R04"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11A05","notation":["11A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiplicative structure; Euclidean algorithm; greatest common divisors"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Axx","notation":["11Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11A07","notation":["11A07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Congruences; primitive roots; residue systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Axx","notation":["11Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11A15","notation":["11A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Power residues, reciprocity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Axx","notation":["11Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11A25","notation":["11A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic functions; related numbers; inversion formulas"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Axx","notation":["11Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11A41","notation":["11A41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Primes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Axx","notation":["11Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11A51","notation":["11A51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Factorization; primality"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Axx","notation":["11Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11A55","notation":["11A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continued fractions"},"scopeNote":{"en":["For approximation results, see 11J70; See also 11K50, 30B70, 40A15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Axx","notation":["11Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11A63","notation":["11A63"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Radix representation; digital problems"},"scopeNote":{"en":["For metric results, see 11K16"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Axx","notation":["11Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11A67","notation":["11A67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other number representations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Axx","notation":["11Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11A99","notation":["11A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Axx","notation":["11Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sequences and sets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B05","notation":["11B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Density, gaps, topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B13","notation":["11B13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Additive bases, including sumsets"},"scopeNote":{"en":["See also 05B10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B25","notation":["11B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic progressions"},"scopeNote":{"en":["See also 11N13"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B30","notation":["11B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic combinatorics; higher degree uniformity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B34","notation":["11B34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representation functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B37","notation":["11B37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Recurrences"},"scopeNote":{"en":["For applications to special functions, see 33-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B39","notation":["11B39"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fibonacci and Lucas numbers and polynomials and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B50","notation":["11B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sequences (mod m)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B57","notation":["11B57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Farey sequences; the sequences 1k , 2k , . . ."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B65","notation":["11B65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Binomial coefficients; factorials; q-identities"},"scopeNote":{"en":["See also 05A10, 05A30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B68","notation":["11B68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bernoulli and Euler numbers and polynomials"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B73","notation":["11B73"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bell and Stirling numbers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B75","notation":["11B75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other combinatorial number theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B83","notation":["11B83"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special sequences and polynomials"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B85","notation":["11B85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automata sequences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11B99","notation":["11B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Bxx","notation":["11Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Cxx","notation":["11Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials and matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11C08","notation":["11C08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials in number theory"},"scopeNote":{"en":["See also 13F20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Cxx","notation":["11Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11C20","notation":["11C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matrices, determinants in number theory"},"scopeNote":{"en":["See also 15B36"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Cxx","notation":["11Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11C99","notation":["11C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Cxx","notation":["11Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Diophantine equations"},"scopeNote":{"en":["See also 11Gxx, 14Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D04","notation":["11D04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear Diophantine equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D07","notation":["11D07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"The Frobenius problem"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D09","notation":["11D09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quadratic and bilinear Diophantine equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D25","notation":["11D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cubic and quartic Diophantine equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D41","notation":["11D41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher degree equations; Fermat’s equation"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D45","notation":["11D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Counting solutions of Diophantine equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D57","notation":["11D57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiplicative and norm form equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D59","notation":["11D59"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Thue-Mahler equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D61","notation":["11D61"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exponential Diophantine equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D68","notation":["11D68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rational numbers as sums of fractions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D72","notation":["11D72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Diophantine equations in many variables"},"scopeNote":{"en":["See also 11P55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D75","notation":["11D75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Diophantine inequalities"},"scopeNote":{"en":["See also 11J25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D79","notation":["11D79"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Congruences in many variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D85","notation":["11D85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representation problems"},"scopeNote":{"en":["See also 11P55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D88","notation":["11D88"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"p-adic and power series fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11D99","notation":["11D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Dxx","notation":["11Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Forms and linear algebraic groups"},"scopeNote":{"en":["See also 19Gxx; For quadratic forms in linear algebra, see 15A63"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E04","notation":["11E04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quadratic forms over general fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E08","notation":["11E08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quadratic forms over local rings and fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E10","notation":["11E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Forms over real fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E12","notation":["11E12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quadratic forms over global rings and fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E16","notation":["11E16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General binary quadratic forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E20","notation":["11E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General ternary and quaternary quadratic forms; forms of more than two variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E25","notation":["11E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sums of squares and representations by other particular quadratic forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E39","notation":["11E39"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bilinear and Hermitian forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E41","notation":["11E41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Class numbers of quadratic and Hermitian forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E45","notation":["11E45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E57","notation":["11E57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical groups"},"scopeNote":{"en":["See also 14Lxx, 20Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E70","notation":["11E70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K-theory of quadratic and Hermitian forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E72","notation":["11E72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Galois cohomology of linear algebraic groups"},"scopeNote":{"en":["See also 20G10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E76","notation":["11E76"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Forms of degree higher than two"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E81","notation":["11E81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic theory of quadratic forms; Witt groups and rings"},"scopeNote":{"en":["See also 19G12, 19G24"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E88","notation":["11E88"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quadratic spaces; Clifford algebras"},"scopeNote":{"en":["See also 15A63, 15A66"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E95","notation":["11E95"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"p-adic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11E99","notation":["11E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Exx","notation":["11Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discontinuous groups and automorphic forms"},"scopeNote":{"en":["See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx; For relations with quadratic forms, see 11E45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F03","notation":["11F03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modular and automorphic functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F06","notation":["11F06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure of modular groups and generalizations; arithmetic groups"},"scopeNote":{"en":["See also 20H05, 20H10, 22E40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F11","notation":["11F11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Holomorphic modular forms of integral weight"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F12","notation":["11F12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphic forms, one variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F20","notation":["11F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dedekind eta function, Dedekind sums"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F22","notation":["11F22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relationship to Lie algebras and finite simple groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F23","notation":["11F23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations with algebraic geometry and topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F25","notation":["11F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hecke-Petersson operators, differential operators (one variable)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F27","notation":["11F27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theta series; Weil representation; theta correspondences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F30","notation":["11F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fourier coefficients of automorphic forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F32","notation":["11F32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modular correspondences, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F33","notation":["11F33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Congruences for modular and p-adic modular forms"},"scopeNote":{"en":["See also 14G20, 22E50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F37","notation":["11F37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Forms of half-integer weight; nonholomorphic modular forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F41","notation":["11F41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces"},"scopeNote":{"en":["See also 14J20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F46","notation":["11F46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F50","notation":["11F50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jacobi forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F52","notation":["11F52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modular forms associated to Drinfel’d modules"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F55","notation":["11F55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other groups and their modular and automorphic forms (several variables)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F60","notation":["11F60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hecke-Petersson operators, differential operators (several variables)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F66","notation":["11F66"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Langlands L-functions; one variable Dirichlet series and functional equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F67","notation":["11F67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special values of automorphic L-series, periods of automorphic forms, cohomology, modular symbols"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F68","notation":["11F68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F70","notation":["11F70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representation-theoretic methods; automorphic representations over local and global fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F72","notation":["11F72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral theory; trace formulas (e.g., that of Selberg)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F75","notation":["11F75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cohomology of arithmetic groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F77","notation":["11F77"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphic forms and their relations with perfectoid spaces"},"scopeNote":{"en":["See also 14G45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F80","notation":["11F80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Galois representations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F85","notation":["11F85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"p-adic theory, local fields"},"scopeNote":{"en":["See also 14G20, 22E50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11F99","notation":["11F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Fxx","notation":["11Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic algebraic geometry (Diophantine geometry)"},"scopeNote":{"en":["See also 11Dxx, 14Gxx, 14Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G05","notation":["11G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic curves over global fields"},"scopeNote":{"en":["See also 14H52"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G07","notation":["11G07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic curves over local fields"},"scopeNote":{"en":["See also 14G20, 14H52"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G09","notation":["11G09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Drinfel’d modules; higher-dimensional motives, etc."},"scopeNote":{"en":["See also 14L05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G10","notation":["11G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abelian varieties of dimension > 1"},"scopeNote":{"en":["See also 14Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G15","notation":["11G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex multiplication and moduli of abelian varieties"},"scopeNote":{"en":["See also 14K22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G16","notation":["11G16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic and modular units"},"scopeNote":{"en":["See also 11R27"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G18","notation":["11G18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic aspects of modular and Shimura varieties"},"scopeNote":{"en":["See also 14G35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G20","notation":["11G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Curves over finite and local fields"},"scopeNote":{"en":["See also 14H25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G25","notation":["11G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Varieties over finite and local fields"},"scopeNote":{"en":["See also 14G15, 14G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G30","notation":["11G30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Curves of arbitrary genus or genus 6= 1 over global fields"},"scopeNote":{"en":["See also 14H25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G32","notation":["11G32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic aspects of dessins d’enfants, Belyı̆ theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G35","notation":["11G35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Varieties over global fields"},"scopeNote":{"en":["See also 14G25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G40","notation":["11G40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture"},"scopeNote":{"en":["See also 14G10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G42","notation":["11G42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic mirror symmetry"},"scopeNote":{"en":["See also 14J33"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G45","notation":["11G45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric class field theory"},"scopeNote":{"en":["See also 11R37, 14C35, 19F05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G50","notation":["11G50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Heights"},"scopeNote":{"en":["See also 14G40, 37P30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G55","notation":["11G55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polylogarithms and relations with K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11G99","notation":["11G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Gxx","notation":["11Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Hxx","notation":["11Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometry of numbers"},"scopeNote":{"en":["For applications in coding theory, see 94B75"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11H06","notation":["11H06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattices and convex bodies (number-theoretic aspects)"},"scopeNote":{"en":["See also 11P21, 52C05, 52C07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Hxx","notation":["11Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11H16","notation":["11H16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonconvex bodies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Hxx","notation":["11Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11H31","notation":["11H31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattice packing and covering (number-theoretic aspects)"},"scopeNote":{"en":["See also 05B40, 52C15, 52C17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Hxx","notation":["11Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11H46","notation":["11H46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Products of linear forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Hxx","notation":["11Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11H50","notation":["11H50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Minima of forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Hxx","notation":["11Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11H55","notation":["11H55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quadratic forms (reduction theory, extreme forms, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Hxx","notation":["11Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11H56","notation":["11H56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphism groups of lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Hxx","notation":["11Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11H60","notation":["11H60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mean value and transfer theorems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Hxx","notation":["11Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11H71","notation":["11H71"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations with coding theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Hxx","notation":["11Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11H99","notation":["11H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Hxx","notation":["11Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Diophantine approximation, transcendental number theory"},"scopeNote":{"en":["See also 11K60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J04","notation":["11J04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homogeneous approximation to one number"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J06","notation":["11J06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Markov and Lagrange spectra and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J13","notation":["11J13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Simultaneous homogeneous approximation, linear forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J17","notation":["11J17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Approximation by numbers from a fixed field"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J20","notation":["11J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inhomogeneous linear forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J25","notation":["11J25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Diophantine inequalities"},"scopeNote":{"en":["See also 11D75"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J54","notation":["11J54"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Small fractional parts of polynomials and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J61","notation":["11J61"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Approximation in non-Archimedean valuations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J68","notation":["11J68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Approximation to algebraic numbers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J70","notation":["11J70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continued fractions and generalizations"},"scopeNote":{"en":["See also 11A55, 11K50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J71","notation":["11J71"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distribution modulo one"},"scopeNote":{"en":["See also 11K06"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J72","notation":["11J72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Irrationality; linear independence over a field"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J81","notation":["11J81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transcendence (general theory)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J82","notation":["11J82"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measures of irrationality and of transcendence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J83","notation":["11J83"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Metric theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J85","notation":["11J85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic independence; Gel’fond’s method"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J86","notation":["11J86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear forms in logarithms; Baker’s method"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J87","notation":["11J87"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Schmidt Subspace Theorem and applications"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J89","notation":["11J89"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transcendence theory of elliptic and abelian functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J91","notation":["11J91"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transcendence theory of other special functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J93","notation":["11J93"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transcendence theory of Drinfel’d and t-modules"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J95","notation":["11J95"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Results involving abelian varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J97","notation":["11J97"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11J99","notation":["11J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Jxx","notation":["11Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probabilistic theory: distribution modulo 1; metric theory of algorithms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K06","notation":["11K06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of distribution modulo 1"},"scopeNote":{"en":["See also 11J71"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K16","notation":["11K16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc."},"scopeNote":{"en":["See also 11A63"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K31","notation":["11K31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special sequences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K36","notation":["11K36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Well-distributed sequences and other variations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K38","notation":["11K38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Irregularities of distribution, discrepancy"},"scopeNote":{"en":["See also 11Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K41","notation":["11K41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuous, p-adic and abstract analogues"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K45","notation":["11K45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pseudo-random numbers; Monte Carlo methods"},"scopeNote":{"en":["See also 65C05, 65C10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K50","notation":["11K50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Metric theory of continued fractions"},"scopeNote":{"en":["See also 11A55, 11J70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K55","notation":["11K55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Metric theory of other algorithms and expansions; measure and Hausdorff dimension"},"scopeNote":{"en":["See also 11N99, 28Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K60","notation":["11K60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Diophantine approximation in probabilistic number theory"},"scopeNote":{"en":["See also 11Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K65","notation":["11K65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic functions in probabilistic number theory"},"scopeNote":{"en":["See also 11Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K70","notation":["11K70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic analysis and almost periodicity in probabilistic number theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11K99","notation":["11K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Kxx","notation":["11Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Lxx","notation":["11Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exponential sums and character sums"},"scopeNote":{"en":["For finite fields, see 11Txx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11L03","notation":["11L03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Trigonometric and exponential sums, general"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Lxx","notation":["11Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11L05","notation":["11L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gauss and Kloosterman sums; generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Lxx","notation":["11Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11L07","notation":["11L07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Estimates on exponential sums"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Lxx","notation":["11Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11L10","notation":["11L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jacobsthal and Brewer sums; other complete character sums"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Lxx","notation":["11Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11L15","notation":["11L15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Weyl sums"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Lxx","notation":["11Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11L20","notation":["11L20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sums over primes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Lxx","notation":["11Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11L26","notation":["11L26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sums over arbitrary intervals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Lxx","notation":["11Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11L40","notation":["11L40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Estimates on character sums"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Lxx","notation":["11Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11L99","notation":["11L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Lxx","notation":["11Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Zeta and L-functions: analytic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11M06","notation":["11M06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"ζ(s) and L(s, χ)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11M20","notation":["11M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real zeros of L(s, χ); results on L(1, χ)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11M26","notation":["11M26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonreal zeros of ζ(s) and L(s, χ); Riemann and other hypotheses"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11M32","notation":["11M32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiple Dirichlet series and zeta functions and multizeta values"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11M35","notation":["11M35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hurwitz and Lerch zeta functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11M36","notation":["11M36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11M38","notation":["11M38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Zeta and L-functions in characteristic p"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11M41","notation":["11M41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other Dirichlet series and zeta functions"},"scopeNote":{"en":["For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; See also 11E45, 11F66, 11F70, 11F72"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11M45","notation":["11M45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Tauberian theorems"},"scopeNote":{"en":["See also 40E05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11M50","notation":["11M50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations with random matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11M55","notation":["11M55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations with noncommutative geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11M99","notation":["11M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Mxx","notation":["11Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiplicative number theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N05","notation":["11N05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distribution of primes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N13","notation":["11N13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Primes in congruence classes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N25","notation":["11N25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distribution of integers with specified multiplicative constraints"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N30","notation":["11N30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Turán theory"},"scopeNote":{"en":["See also 30Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N32","notation":["11N32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Primes represented by polynomials; other multiplicative structures of polynomial values"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N35","notation":["11N35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sieves"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N36","notation":["11N36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of sieve methods"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N37","notation":["11N37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic results on arithmetic functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N45","notation":["11N45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic results on counting functions for algebraic and topological structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N56","notation":["11N56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rate of growth of arithmetic functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N60","notation":["11N60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distribution functions associated with additive and positive multiplicative functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N64","notation":["11N64"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other results on the distribution of values or the characterization of arithmetic functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N69","notation":["11N69"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distribution of integers in special residue classes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N75","notation":["11N75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of automorphic functions and forms to multiplicative problems"},"scopeNote":{"en":["See also 11Fxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N80","notation":["11N80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized primes and integers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11N99","notation":["11N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Nxx","notation":["11Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Pxx","notation":["11Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Additive number theory; partitions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11P05","notation":["11P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Waring’s problem and variants"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Pxx","notation":["11Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11P21","notation":["11P21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattice points in specified regions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Pxx","notation":["11Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11P32","notation":["11P32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Goldbach-type theorems; other additive questions involving primes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Pxx","notation":["11Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11P55","notation":["11P55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of the Hardy-Littlewood method"},"scopeNote":{"en":["See also 11D85"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Pxx","notation":["11Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11P70","notation":["11P70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems of additive number theory, including sumsets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Pxx","notation":["11Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11P81","notation":["11P81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elementary theory of partitions"},"scopeNote":{"en":["See also 05A17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Pxx","notation":["11Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11P82","notation":["11P82"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytic theory of partitions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Pxx","notation":["11Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11P83","notation":["11P83"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partitions; congruences and congruential restrictions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Pxx","notation":["11Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11P84","notation":["11P84"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partition identities; identities of Rogers-Ramanujan type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Pxx","notation":["11Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11P99","notation":["11P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Pxx","notation":["11Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic number theory: global fields"},"scopeNote":{"en":["For complex multiplication, see 11G15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R04","notation":["11R04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic numbers; rings of algebraic integers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R06","notation":["11R06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PV-numbers and generalizations; other special algebraic numbers; Mahler measure"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R09","notation":["11R09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials (irreducibility, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R11","notation":["11R11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quadratic extensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R16","notation":["11R16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cubic and quartic extensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R18","notation":["11R18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cyclotomic extensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R20","notation":["11R20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other abelian and metabelian extensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R21","notation":["11R21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other number fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R23","notation":["11R23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Iwasawa theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R27","notation":["11R27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Units and factorization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R29","notation":["11R29"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Class numbers, class groups, discriminants"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R32","notation":["11R32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Galois theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R33","notation":["11R33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral representations related to algebraic numbers; Galois module structure of rings of integers"},"scopeNote":{"en":["See also 20C10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R34","notation":["11R34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Galois cohomology"},"scopeNote":{"en":["See also 12Gxx, 19A31"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R37","notation":["11R37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Class field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R39","notation":["11R39"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Langlands-Weil conjectures, nonabelian class field theory"},"scopeNote":{"en":["See also 11Fxx, 22E55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R42","notation":["11R42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Zeta functions and L-functions of number fields"},"scopeNote":{"en":["See also 11M41, 19F27"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R44","notation":["11R44"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distribution of prime ideals"},"scopeNote":{"en":["See also 11N05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R45","notation":["11R45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Density theorems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R47","notation":["11R47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other analytic theory"},"scopeNote":{"en":["See also 11Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R52","notation":["11R52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quaternion and other division algebras: arithmetic, zeta functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R54","notation":["11R54"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other algebras and orders, and their zeta and L-functions"},"scopeNote":{"en":["See also 11S45, 16Hxx, 16Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R56","notation":["11R56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Adèle rings and groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R58","notation":["11R58"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic theory of algebraic function fields"},"scopeNote":{"en":["See also 14-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R59","notation":["11R59"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Zeta functions and L-functions of function fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R60","notation":["11R60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cyclotomic function fields (class groups, Bernoulli objects, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R65","notation":["11R65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Class groups and Picard groups of orders"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R70","notation":["11R70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K-theory of global fields"},"scopeNote":{"en":["See also 19Fxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R80","notation":["11R80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Totally real fields"},"scopeNote":{"en":["See also 12J15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11R99","notation":["11R99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Rxx","notation":["11Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic number theory: local and p-adic fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S05","notation":["11S05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S15","notation":["11S15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ramification and extension theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S20","notation":["11S20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Galois theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S23","notation":["11S23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral representations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S25","notation":["11S25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Galois cohomology"},"scopeNote":{"en":["See also 12Gxx, 16H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S31","notation":["11S31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Class field theory; p-adic formal groups"},"scopeNote":{"en":["See also 14L05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S37","notation":["11S37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Langlands-Weil conjectures, nonabelian class field theory"},"scopeNote":{"en":["See also 11Fxx, 22E50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S40","notation":["11S40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Zeta functions and L-functions"},"scopeNote":{"en":["See also 11M41, 19F27"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S45","notation":["11S45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebras and orders, and their zeta functions"},"scopeNote":{"en":["See also 11R52, 11R54, 16Hxx, 16Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S70","notation":["11S70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K-theory of local fields"},"scopeNote":{"en":["See also 19Fxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S80","notation":["11S80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S82","notation":["11S82"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Non-Archimedean dynamical systems"},"scopeNote":{"en":["See mainly 37Pxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S85","notation":["11S85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other nonanalytic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S90","notation":["11S90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Prehomogeneous vector spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11S99","notation":["11S99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Sxx","notation":["11Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Txx","notation":["11Txx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite fields and commutative rings (number-theoretic aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11T06","notation":["11T06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials over finite fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Txx","notation":["11Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11T22","notation":["11T22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cyclotomy"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Txx","notation":["11Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11T23","notation":["11T23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exponential sums"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Txx","notation":["11Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11T24","notation":["11T24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other character sums and Gauss sums"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Txx","notation":["11Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11T30","notation":["11T30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure theory for finite fields and commutative rings, number-theoretic aspects"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Txx","notation":["11Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11T55","notation":["11T55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic theory of polynomial rings over finite fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Txx","notation":["11Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11T60","notation":["11T60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite upper half-planes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Txx","notation":["11Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11T71","notation":["11T71"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic coding theory; cryptography (number-theoretic aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Txx","notation":["11Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11T99","notation":["11T99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Txx","notation":["11Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Uxx","notation":["11Uxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connections of number theory and logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11U05","notation":["11U05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Decidability (number-theoretic aspects)"},"scopeNote":{"en":["See also 03B25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Uxx","notation":["11Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11U07","notation":["11U07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ultraproducts (number-theoretic aspects)"},"scopeNote":{"en":["See also 03C20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Uxx","notation":["11Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11U09","notation":["11U09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Model theory (number-theoretic aspects)"},"scopeNote":{"en":["See also 03Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Uxx","notation":["11Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11U10","notation":["11U10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonstandard arithmetic (number-theoretic aspects)"},"scopeNote":{"en":["See also 03H15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Uxx","notation":["11Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11U99","notation":["11U99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Uxx","notation":["11Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Yxx","notation":["11Yxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational number theory"},"scopeNote":{"en":["For software etc., see 11-04"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Y05","notation":["11Y05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Factorization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Yxx","notation":["11Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Y11","notation":["11Y11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Primality"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Yxx","notation":["11Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Y16","notation":["11Y16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Number-theoretic algorithms; complexity"},"scopeNote":{"en":["See also 68Q25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Yxx","notation":["11Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Y35","notation":["11Y35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytic computations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Yxx","notation":["11Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Y40","notation":["11Y40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic number theory computations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Yxx","notation":["11Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Y50","notation":["11Y50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computer solution of Diophantine equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Yxx","notation":["11Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Y55","notation":["11Y55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Calculation of integer sequences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Yxx","notation":["11Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Y60","notation":["11Y60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Evaluation of number-theoretic constants"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Yxx","notation":["11Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Y65","notation":["11Y65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continued fraction calculations (number-theoretic aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Yxx","notation":["11Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Y70","notation":["11Y70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Values of arithmetic functions; tables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Yxx","notation":["11Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Y99","notation":["11Y99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Yxx","notation":["11Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Zxx","notation":["11Zxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Miscellaneous applications of number theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11-XX","notation":["11-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Z05","notation":["11Z05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Miscellaneous applications of number theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Zxx","notation":["11Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/11Z99","notation":["11Z99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/11Zxx","notation":["11Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Field theory and polynomials"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12-00","notation":["12-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12-01","notation":["12-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12-02","notation":["12-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12-03","notation":["12-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of field theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12-04","notation":["12-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12-06","notation":["12-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12-08","notation":["12-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12-11","notation":["12-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12Dxx","notation":["12Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real and complex fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12D05","notation":["12D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials in real and complex fields: factorization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Dxx","notation":["12Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12D10","notation":["12D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials in real and complex fields: location of zeros (algebraic theorems)"},"scopeNote":{"en":["For the analytic theory, see 26C10, 30C15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Dxx","notation":["12Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12D15","notation":["12D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)"},"scopeNote":{"en":["See also 11Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Dxx","notation":["12Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12D99","notation":["12D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Dxx","notation":["12Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12Exx","notation":["12Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12E05","notation":["12E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials in general fields (irreducibility, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Exx","notation":["12Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12E10","notation":["12E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special polynomials in general fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Exx","notation":["12Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12E12","notation":["12E12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equations in general fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Exx","notation":["12Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12E15","notation":["12E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Skew fields, division rings"},"scopeNote":{"en":["See also 11R52, 11R54, 11S45, 16Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Exx","notation":["12Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12E20","notation":["12E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite fields (field-theoretic aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Exx","notation":["12Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12E25","notation":["12E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hilbertian fields; Hilbert’s irreducibility theorem"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Exx","notation":["12Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12E30","notation":["12E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Field arithmetic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Exx","notation":["12Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12E99","notation":["12E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Exx","notation":["12Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12Fxx","notation":["12Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Field extensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12F05","notation":["12F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic field extensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Fxx","notation":["12Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12F10","notation":["12F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Separable extensions, Galois theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Fxx","notation":["12Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12F12","notation":["12F12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse Galois theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Fxx","notation":["12Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12F15","notation":["12F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inseparable field extensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Fxx","notation":["12Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12F20","notation":["12F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transcendental field extensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Fxx","notation":["12Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12F99","notation":["12F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Fxx","notation":["12Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12Gxx","notation":["12Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological methods (field theory)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12G05","notation":["12G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Galois cohomology"},"scopeNote":{"en":["See also 14F22, 16Hxx, 16K50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Gxx","notation":["12Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12G10","notation":["12G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cohomological dimension of fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Gxx","notation":["12Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12G99","notation":["12G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Gxx","notation":["12Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12Hxx","notation":["12Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential and difference algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12H05","notation":["12H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential algebra"},"scopeNote":{"en":["See also 13Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Hxx","notation":["12Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12H10","notation":["12H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Difference algebra"},"scopeNote":{"en":["See also 39Axx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Hxx","notation":["12Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12H20","notation":["12H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract differential equations"},"scopeNote":{"en":["See also 34Mxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Hxx","notation":["12Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12H25","notation":["12H25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"p-adic differential equations"},"scopeNote":{"en":["See also 11S80, 14G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Hxx","notation":["12Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12H99","notation":["12H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Hxx","notation":["12Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12Jxx","notation":["12Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12J05","notation":["12J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Normed fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Jxx","notation":["12Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12J10","notation":["12J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Valued fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Jxx","notation":["12Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12J12","notation":["12J12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Formally p-adic fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Jxx","notation":["12Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12J15","notation":["12J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Jxx","notation":["12Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12J17","notation":["12J17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological semifields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Jxx","notation":["12Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12J20","notation":["12J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General valuation theory for fields"},"scopeNote":{"en":["See also 13A18"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Jxx","notation":["12Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12J25","notation":["12J25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Non-Archimedean valued fields"},"scopeNote":{"en":["See also 30G06, 32P05, 46S10, 47S10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Jxx","notation":["12Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12J27","notation":["12J27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Krasner-Tate algebras"},"scopeNote":{"en":["See mainly 32P05; see also 46S10, 47S10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Jxx","notation":["12Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12J99","notation":["12J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Jxx","notation":["12Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12Kxx","notation":["12Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12K05","notation":["12K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Near-fields"},"scopeNote":{"en":["See also 16Y30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Kxx","notation":["12Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12K10","notation":["12K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semifields"},"scopeNote":{"en":["See also 16Y60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Kxx","notation":["12Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12K99","notation":["12K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Kxx","notation":["12Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12Lxx","notation":["12Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connections between field theory and logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12-XX","notation":["12-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12L05","notation":["12L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Decidability and field theory"},"scopeNote":{"en":["See also 03B25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Lxx","notation":["12Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12L10","notation":["12L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ultraproducts and field theory"},"scopeNote":{"en":["See also 03C20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Lxx","notation":["12Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12L12","notation":["12L12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Model theory of fields"},"scopeNote":{"en":["See also 03C60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Lxx","notation":["12Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12L15","notation":["12L15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonstandard arithmetic and field theory"},"scopeNote":{"en":["See also 03H15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Lxx","notation":["12Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/12L99","notation":["12L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/12Lxx","notation":["12Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutative algebra"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13-00","notation":["13-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to commutative algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13-01","notation":["13-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13-02","notation":["13-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to commutative algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13-03","notation":["13-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of commutative algebra"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13-04","notation":["13-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to commutative algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13-06","notation":["13-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to commutative algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13-11","notation":["13-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to commutative algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Axx","notation":["13Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General commutative ring theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13A02","notation":["13A02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graded rings"},"scopeNote":{"en":["See also 16W50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Axx","notation":["13Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13A05","notation":["13A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Divisibility and factorizations in commutative rings"},"scopeNote":{"en":["See also 13F15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Axx","notation":["13Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13A15","notation":["13A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ideals and multiplicative ideal theory in commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Axx","notation":["13Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13A18","notation":["13A18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Valuations and their generalizations for commutative rings"},"scopeNote":{"en":["See also 12J20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Axx","notation":["13Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13A30","notation":["13A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Axx","notation":["13Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13A35","notation":["13A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure"},"scopeNote":{"en":["See also 13B22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Axx","notation":["13Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13A50","notation":["13A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Actions of groups on commutative rings; invariant theory"},"scopeNote":{"en":["See also 14L24"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Axx","notation":["13Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13A70","notation":["13A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.)"},"scopeNote":{"en":["See also 05C25, 05E40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Axx","notation":["13Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13A99","notation":["13A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Axx","notation":["13Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Bxx","notation":["13Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutative ring extensions and related topics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13B02","notation":["13B02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extension theory of commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Bxx","notation":["13Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13B05","notation":["13B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Galois theory and commutative ring extensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Bxx","notation":["13Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13B10","notation":["13B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Morphisms of commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Bxx","notation":["13Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13B21","notation":["13B21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral dependence in commutative rings; going up, going down"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Bxx","notation":["13Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13B22","notation":["13B22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral closure of commutative rings and ideals ; integrally closed rings, related rings (Japanese, etc.)"},"scopeNote":{"en":["See also 13A35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Bxx","notation":["13Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13B25","notation":["13B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials over commutative rings"},"scopeNote":{"en":["See also 11C08, 11T06, 13F20, 13M10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Bxx","notation":["13Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13B30","notation":["13B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rings of fractions and localization for commutative rings"},"scopeNote":{"en":["See also 16S85"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Bxx","notation":["13Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13B35","notation":["13B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Completion of commutative rings"},"scopeNote":{"en":["See also 13J10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Bxx","notation":["13Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13B40","notation":["13B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Étale and flat extensions; Henselization; Artin approximation"},"scopeNote":{"en":["See also 13J15, 14B12, 14B25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Bxx","notation":["13Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13B99","notation":["13B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Bxx","notation":["13Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of modules and ideals in commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13C05","notation":["13C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure, classification theorems for modules and ideals in commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13C10","notation":["13C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Projective and free modules and ideals in commutative rings"},"scopeNote":{"en":["See also 19A13"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13C11","notation":["13C11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Injective and flat modules and ideals in commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13C12","notation":["13C12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Torsion modules and ideals in commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13C13","notation":["13C13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other special types of modules and ideals in commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13C14","notation":["13C14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cohen-Macaulay modules"},"scopeNote":{"en":["See also 13H10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13C15","notation":["13C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dimension theory, depth, related commutative rings (catenary, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13C20","notation":["13C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Class groups"},"scopeNote":{"en":["See also 11R29"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13C40","notation":["13C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linkage, complete intersections and determinantal ideals"},"scopeNote":{"en":["See also 14M06, 14M10, 14M12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13C60","notation":["13C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Module categories and commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13C70","notation":["13C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of modules and ideals in commutative rings described by combinatorial properties"},"scopeNote":{"en":["See also 05C25, 05E40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13C99","notation":["13C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Cxx","notation":["13Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological methods in commutative ring theory"},"scopeNote":{"en":["For noncommutative rings, see 16Exx; for general categories, see 18Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13D02","notation":["13D02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Syzygies, resolutions, complexes and commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13D03","notation":["13D03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13D05","notation":["13D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological dimension and commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13D07","notation":["13D07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological functors on modules of commutative rings (Tor, Ext, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13D09","notation":["13D09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Derived categories and commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13D10","notation":["13D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deformations and infinitesimal methods in commutative ring theory"},"scopeNote":{"en":["See also 14B10, 14B12, 14D15, 32Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13D15","notation":["13D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Grothendieck groups, K-theory and commutative rings"},"scopeNote":{"en":["See also 14C35, 18F30, 19Axx, 19D50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13D22","notation":["13D22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological conjectures (intersection theorems) in commutative ring theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13D30","notation":["13D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Torsion theory for commutative rings"},"scopeNote":{"en":["See also 13C12, 18E40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13D40","notation":["13D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13D45","notation":["13D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local cohomology and commutative rings"},"scopeNote":{"en":["See also 14B15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13D99","notation":["13D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Dxx","notation":["13Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Exx","notation":["13Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chain conditions, finiteness conditions in commutative ring theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13E05","notation":["13E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutative Noetherian rings and modules"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Exx","notation":["13Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13E10","notation":["13E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutative Artinian rings and modules, finite-dimensional algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Exx","notation":["13Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13E15","notation":["13E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutative rings and modules of finite generation or presentation; number of generators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Exx","notation":["13Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13E99","notation":["13E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Exx","notation":["13Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic rings and other special commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F05","notation":["13F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dedekind, Prüfer, Krull and Mori rings and their generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F07","notation":["13F07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Euclidean rings and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F10","notation":["13F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Principal ideal rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F15","notation":["13F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial)"},"scopeNote":{"en":["See also 13A05, 14M05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F20","notation":["13F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomial rings and ideals; rings of integer-valued polynomials"},"scopeNote":{"en":["See also 11C08, 13B25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F25","notation":["13F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Formal power series rings"},"scopeNote":{"en":["See also 13J05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F30","notation":["13F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Valuation rings"},"scopeNote":{"en":["See also 13A18"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F35","notation":["13F35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Witt vectors and related rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F40","notation":["13F40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Excellent rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F45","notation":["13F45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Seminormal rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F50","notation":["13F50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rings with straightening laws, Hodge algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F55","notation":["13F55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes"},"scopeNote":{"en":["See also 55U10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F60","notation":["13F60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cluster algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F65","notation":["13F65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutative rings defined by binomial ideals, toric rings, etc."},"scopeNote":{"en":["See also 14M25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F70","notation":["13F70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other commutative rings defined by combinatorial properties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13F99","notation":["13F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Fxx","notation":["13Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Gxx","notation":["13Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral domains"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13G05","notation":["13G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral domains"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Gxx","notation":["13Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13G99","notation":["13G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Gxx","notation":["13Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Hxx","notation":["13Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local rings and semilocal rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13H05","notation":["13H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Regular local rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Hxx","notation":["13Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13H10","notation":["13H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)"},"scopeNote":{"en":["See also 14M05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Hxx","notation":["13Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13H15","notation":["13H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiplicity theory and related topics"},"scopeNote":{"en":["See also 14C17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Hxx","notation":["13Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13H99","notation":["13H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Hxx","notation":["13Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Jxx","notation":["13Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological rings and modules"},"scopeNote":{"en":["See also 16W60, 16W80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13J05","notation":["13J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Power series rings"},"scopeNote":{"en":["See also 13F25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Jxx","notation":["13Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13J07","notation":["13J07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytical algebras and rings"},"scopeNote":{"en":["See also 32B05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Jxx","notation":["13Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13J10","notation":["13J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complete rings, completion"},"scopeNote":{"en":["See also 13B35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Jxx","notation":["13Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13J15","notation":["13J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Henselian rings"},"scopeNote":{"en":["See also 13B40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Jxx","notation":["13Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13J20","notation":["13J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global topological rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Jxx","notation":["13Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13J25","notation":["13J25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered rings"},"scopeNote":{"en":["See also 06F25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Jxx","notation":["13Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13J30","notation":["13J30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real algebra"},"scopeNote":{"en":["See also 12D15, 14Pxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Jxx","notation":["13Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13J99","notation":["13J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Jxx","notation":["13Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Lxx","notation":["13Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of logic to commutative algebra"},"scopeNote":{"en":["See also 03Cxx, 03Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13L05","notation":["13L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of logic to commutative algebra"},"scopeNote":{"en":["See also 03Cxx, 03Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Lxx","notation":["13Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13L99","notation":["13L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Lxx","notation":["13Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Mxx","notation":["13Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite commutative rings"},"scopeNote":{"en":["For number-theoretic aspects, see 11Txx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13M05","notation":["13M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure of finite commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Mxx","notation":["13Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13M10","notation":["13M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials and finite commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Mxx","notation":["13Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13M99","notation":["13M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Mxx","notation":["13Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Nxx","notation":["13Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential algebra"},"scopeNote":{"en":["See also 12H05, 14F10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13N05","notation":["13N05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modules of differentials"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Nxx","notation":["13Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13N10","notation":["13N10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutative rings of differential operators and their modules"},"scopeNote":{"en":["See also 16S32, 32C38"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Nxx","notation":["13Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13N15","notation":["13N15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Derivations and commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Nxx","notation":["13Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13N99","notation":["13N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Nxx","notation":["13Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13Pxx","notation":["13Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational aspects and applications of commutative rings"},"scopeNote":{"en":["See also 14Qxx, 68W30; For software etc., see 13-04"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13-XX","notation":["13-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13P05","notation":["13P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials, factorization in commutative rings"},"scopeNote":{"en":["See also 12-08"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Pxx","notation":["13Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13P10","notation":["13P10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Pxx","notation":["13Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13P15","notation":["13P15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Solving polynomial systems; resultants"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Pxx","notation":["13Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13P20","notation":["13P20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational homological algebra"},"scopeNote":{"en":["See also 13Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Pxx","notation":["13Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13P25","notation":["13P25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Pxx","notation":["13Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/13P99","notation":["13P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/13Pxx","notation":["13Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic geometry"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14-00","notation":["14-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14-01","notation":["14-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14-02","notation":["14-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14-03","notation":["14-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of algebraic geometry"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14-04","notation":["14-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14-06","notation":["14-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14-11","notation":["14-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Axx","notation":["14Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations of algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14A05","notation":["14A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relevant commutative algebra"},"scopeNote":{"en":["See also 13-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Axx","notation":["14Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14A10","notation":["14A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Varieties and morphisms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Axx","notation":["14Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14A15","notation":["14A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Schemes and morphisms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Axx","notation":["14Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14A20","notation":["14A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations (algebraic spaces, stacks)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Axx","notation":["14Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14A21","notation":["14A21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logarithmic algebraic geometry, log schemes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Axx","notation":["14Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14A22","notation":["14A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative algebraic geometry"},"scopeNote":{"en":["See also 16S38"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Axx","notation":["14Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14A23","notation":["14A23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometry over the field with one element"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Axx","notation":["14Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14A25","notation":["14A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elementary questions in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Axx","notation":["14Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14A30","notation":["14A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.)"},"scopeNote":{"en":["For categorical aspects, see 18Fxx, 18Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Axx","notation":["14Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14A99","notation":["14A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Axx","notation":["14Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Bxx","notation":["14Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local theory in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14B05","notation":["14B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singularities in algebraic geometry"},"scopeNote":{"en":["See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Bxx","notation":["14Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14B07","notation":["14B07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deformations of singularities"},"scopeNote":{"en":["See also 14D15, 32S30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Bxx","notation":["14Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14B10","notation":["14B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinitesimal methods in algebraic geometry"},"scopeNote":{"en":["See also 13D10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Bxx","notation":["14Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14B12","notation":["14B12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local deformation theory, Artin approximation, etc."},"scopeNote":{"en":["See also 13B40, 13D10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Bxx","notation":["14Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14B15","notation":["14B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local cohomology and algebraic geometry"},"scopeNote":{"en":["See also 13D45, 32C36"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Bxx","notation":["14Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14B20","notation":["14B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Formal neighborhoods in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Bxx","notation":["14Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14B25","notation":["14B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local structure of morphisms in algebraic geometry: étale, flat, etc."},"scopeNote":{"en":["See also 13B40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Bxx","notation":["14Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14B99","notation":["14B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Bxx","notation":["14Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cycles and subschemes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14C05","notation":["14C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Parametrization (Chow and Hilbert schemes)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14C15","notation":["14C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"(Equivariant) Chow groups and rings; motives"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14C17","notation":["14C17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry"},"scopeNote":{"en":["See also 13H15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14C20","notation":["14C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Divisors, linear systems, invertible sheaves"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14C21","notation":["14C21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pencils, nets, webs in algebraic geometry"},"scopeNote":{"en":["See also 53A60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14C22","notation":["14C22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Picard groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14C25","notation":["14C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic cycles"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14C30","notation":["14C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transcendental methods, Hodge theory (algebro-geometric aspects) , Hodge conjecture"},"scopeNote":{"en":["See also 14D07, 32G20, 32J25, 32S35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14C34","notation":["14C34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Torelli problem"},"scopeNote":{"en":["See also 32G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14C35","notation":["14C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of methods of algebraic K-theory in algebraic geometry"},"scopeNote":{"en":["See also 19Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14C40","notation":["14C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Riemann-Roch theorems"},"scopeNote":{"en":["See also 19E20, 19L10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14C99","notation":["14C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Cxx","notation":["14Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Dxx","notation":["14Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Families, fibrations in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14D05","notation":["14D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure of families (Picard-Lefschetz, monodromy, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Dxx","notation":["14Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14D06","notation":["14D06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fibrations, degenerations in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Dxx","notation":["14Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14D07","notation":["14D07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variation of Hodge structures (algebro-geometric aspects)"},"scopeNote":{"en":["See also 32G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Dxx","notation":["14Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14D10","notation":["14D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic ground fields (finite, local, global) and families or fibrations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Dxx","notation":["14Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14D15","notation":["14D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Formal methods and deformations in algebraic geometry"},"scopeNote":{"en":["See also 13D10, 14B07, 32Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Dxx","notation":["14Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14D20","notation":["14D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic moduli problems, moduli of vector bundles"},"scopeNote":{"en":["For analytic moduli problems, see 32G13"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Dxx","notation":["14Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14D21","notation":["14D21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)"},"scopeNote":{"en":["See also 32L25, 81Txx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Dxx","notation":["14Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14D22","notation":["14D22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fine and coarse moduli spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Dxx","notation":["14Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14D23","notation":["14D23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stacks and moduli problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Dxx","notation":["14Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14D24","notation":["14D24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric Langlands program (algebro-geometric aspects)"},"scopeNote":{"en":["See also 22E57"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Dxx","notation":["14Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14D99","notation":["14D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Dxx","notation":["14Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Exx","notation":["14Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Birational geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14E05","notation":["14E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rational and birational maps"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Exx","notation":["14Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14E07","notation":["14E07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Birational automorphisms, Cremona group and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Exx","notation":["14Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14E08","notation":["14E08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rationality questions in algebraic geometry"},"scopeNote":{"en":["See also 14M20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Exx","notation":["14Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14E15","notation":["14E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global theory and resolution of singularities (algebro-geometric aspects)"},"scopeNote":{"en":["See also 14B05, 32S20, 32S45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Exx","notation":["14Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14E16","notation":["14E16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"McKay correspondence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Exx","notation":["14Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14E18","notation":["14E18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arcs and motivic integration"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Exx","notation":["14Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14E20","notation":["14E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Coverings in algebraic geometry"},"scopeNote":{"en":["See also 14H30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Exx","notation":["14Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14E22","notation":["14E22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ramification problems in algebraic geometry"},"scopeNote":{"en":["See also 11S15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Exx","notation":["14Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14E25","notation":["14E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Embeddings in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Exx","notation":["14Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14E30","notation":["14E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Minimal model program (Mori theory, extremal rays)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Exx","notation":["14Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14E99","notation":["14E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Exx","notation":["14Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"(Co)homology theory in algebraic geometry"},"scopeNote":{"en":["See also 13Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F06","notation":["14F06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sheaves in algebraic geometry"},"scopeNote":{"en":["See also 14F07, 14H60, 14J60, 18F20, 32Lxx, 46M20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F07","notation":["14F07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Derived categories of sheaves, dg categories, and related constructions in algebraic geometry"},"scopeNote":{"en":["See also 14A30, 14F06, 18Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F10","notation":["14F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials"},"scopeNote":{"en":["See also 13Nxx, 32C38"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F17","notation":["14F17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vanishing theorems in algebraic geometry"},"scopeNote":{"en":["See also 32L20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F18","notation":["14F18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiplier ideals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F20","notation":["14F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Étale and other Grothendieck topologies and (co)homologies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F22","notation":["14F22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Brauer groups of schemes"},"scopeNote":{"en":["See also 12G05, 16K50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F25","notation":["14F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical real and complex (co)homology in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F30","notation":["14F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"p-adic cohomology, crystalline cohomology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F35","notation":["14F35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homotopy theory and fundamental groups in algebraic geometry"},"scopeNote":{"en":["See also 14H30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F40","notation":["14F40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"de Rham cohomology and algebraic geometry"},"scopeNote":{"en":["See also 14C30, 32C35, 32L10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F42","notation":["14F42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Motivic cohomology; motivic homotopy theory"},"scopeNote":{"en":["See also 19E15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F43","notation":["14F43"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F45","notation":["14F45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological properties in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14F99","notation":["14F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Fxx","notation":["14Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic problems in algebraic geometry; Diophantine geometry"},"scopeNote":{"en":["See also 11Dxx, 11Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G05","notation":["14G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rational points"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G10","notation":["14G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)"},"scopeNote":{"en":["See also 11G40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G12","notation":["14G12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hasse principle, weak and strong approximation, Brauer-Manin obstruction"},"scopeNote":{"en":["See also 14F22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G15","notation":["14G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite ground fields in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G17","notation":["14G17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Positive characteristic ground fields in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G20","notation":["14G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local ground fields in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G22","notation":["14G22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rigid analytic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G25","notation":["14G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global ground fields in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G27","notation":["14G27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other nonalgebraically closed ground fields in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G32","notation":["14G32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G35","notation":["14G35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modular and Shimura varieties"},"scopeNote":{"en":["See also 11F41, 11F46, 11G18"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G40","notation":["14G40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic varieties and schemes; Arakelov theory; heights"},"scopeNote":{"en":["See also 11G50, 37P30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G45","notation":["14G45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perfectoid spaces and mixed characteristic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G50","notation":["14G50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications to coding theory and cryptography of arithmetic geometry"},"scopeNote":{"en":["See also 94A60, 94B27, 94B40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14G99","notation":["14G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Gxx","notation":["14Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Curves in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H05","notation":["14H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic functions and function fields in algebraic geometry"},"scopeNote":{"en":["See also 11R58"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H10","notation":["14H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Families, moduli of curves (algebraic)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H15","notation":["14H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Families, moduli of curves (analytic)"},"scopeNote":{"en":["See also 30F10, 32G15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H20","notation":["14H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singularities of curves, local rings"},"scopeNote":{"en":["See also 13Hxx, 14B05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H25","notation":["14H25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic ground fields for curves"},"scopeNote":{"en":["See also 11Dxx, 11G05, 14Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H30","notation":["14H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Coverings of curves, fundamental group"},"scopeNote":{"en":["See also 14E20, 14F35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H37","notation":["14H37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphisms of curves"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H40","notation":["14H40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jacobians, Prym varieties"},"scopeNote":{"en":["See also 32G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H42","notation":["14H42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theta functions and curves; Schottky problem"},"scopeNote":{"en":["See also 14K25, 32G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H45","notation":["14H45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special algebraic curves and curves of low genus"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H50","notation":["14H50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Plane and space curves"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H51","notation":["14H51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special divisors on curves (gonality, Brill-Noether theory)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H52","notation":["14H52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic curves"},"scopeNote":{"en":["See also 11G05, 11G07, 14Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H55","notation":["14H55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Riemann surfaces; Weierstrass points; gap sequences"},"scopeNote":{"en":["See also 30Fxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H57","notation":["14H57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dessins d’enfants theory"},"scopeNote":{"en":["For arithmetic aspects, see 11G32"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H60","notation":["14H60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vector bundles on curves and their moduli"},"scopeNote":{"en":["See also 14D20, 14F06, 14J60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H70","notation":["14H70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relationships between algebraic curves and integrable systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H81","notation":["14H81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relationships between algebraic curves and physics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14H99","notation":["14H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Hxx","notation":["14Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Surfaces and higher-dimensional varieties"},"scopeNote":{"en":["For analytic theory, see 32Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J10","notation":["14J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Families, moduli, classification: algebraic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J15","notation":["14J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Moduli, classification: analytic theory; relations with modular forms"},"scopeNote":{"en":["See also 32G13"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J17","notation":["14J17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singularities of surfaces or higher-dimensional varieties"},"scopeNote":{"en":["See also 14B05, 14E15, 32S05, 32S25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J20","notation":["14J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic ground fields for surfaces or higher-dimensional varieties"},"scopeNote":{"en":["See also 11Dxx, 11G25, 11G35, 14Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J25","notation":["14J25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special surfaces"},"scopeNote":{"en":["For Hilbert modular surfaces, see 14G35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J26","notation":["14J26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rational and ruled surfaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J27","notation":["14J27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic surfaces, elliptic or Calabi-Yau fibrations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J28","notation":["14J28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K3 surfaces and Enriques surfaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J29","notation":["14J29"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Surfaces of general type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J30","notation":["14J30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"3-folds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J32","notation":["14J32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Calabi-Yau manifolds (algebro-geometric aspects)"},"scopeNote":{"en":["See also 32Q25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J33","notation":["14J33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mirror symmetry (algebro-geometric aspects)"},"scopeNote":{"en":["See also 11G42, 53D37"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J35","notation":["14J35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"4-folds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J40","notation":["14J40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"n-folds (n > 4)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J42","notation":["14J42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Holomorphic symplectic varieties, hyper-Kähler varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J45","notation":["14J45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fano varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J50","notation":["14J50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphisms of surfaces and higher-dimensional varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J60","notation":["14J60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vector bundles on surfaces and higher-dimensional varieties, and their moduli"},"scopeNote":{"en":["See also 14D20, 14F06, 14H60, 32Lxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J70","notation":["14J70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hypersurfaces and algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J80","notation":["14J80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J81","notation":["14J81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relationships with physics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14J99","notation":["14J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Jxx","notation":["14Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Kxx","notation":["14Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abelian varieties and schemes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14K02","notation":["14K02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Isogeny"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Kxx","notation":["14Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14K05","notation":["14K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic theory of abelian varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Kxx","notation":["14Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14K10","notation":["14K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic moduli of abelian varieties, classification"},"scopeNote":{"en":["See also 11G15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Kxx","notation":["14Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14K12","notation":["14K12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subvarieties of abelian varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Kxx","notation":["14Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14K15","notation":["14K15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic ground fields for abelian varieties"},"scopeNote":{"en":["See also 11Dxx, 11Fxx, 11G10, 14Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Kxx","notation":["14Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14K20","notation":["14K20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytic theory of abelian varieties; abelian integrals and differentials"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Kxx","notation":["14Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14K22","notation":["14K22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex multiplication and abelian varieties"},"scopeNote":{"en":["See also 11G15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Kxx","notation":["14Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14K25","notation":["14K25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theta functions and abelian varieties"},"scopeNote":{"en":["See also 14H42"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Kxx","notation":["14Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14K30","notation":["14K30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Picard schemes, higher Jacobians"},"scopeNote":{"en":["See also 14H40, 32G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Kxx","notation":["14Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14K99","notation":["14K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Kxx","notation":["14Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Lxx","notation":["14Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic groups"},"scopeNote":{"en":["For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14L05","notation":["14L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Formal groups, p-divisible groups"},"scopeNote":{"en":["See also 55N22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Lxx","notation":["14Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14L10","notation":["14L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Lxx","notation":["14Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14L15","notation":["14L15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group schemes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Lxx","notation":["14Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14L17","notation":["14L17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Affine algebraic groups, hyperalgebra constructions"},"scopeNote":{"en":["See also 17B45, 18C40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Lxx","notation":["14Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14L24","notation":["14L24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric invariant theory"},"scopeNote":{"en":["See also 13A50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Lxx","notation":["14Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14L30","notation":["14L30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group actions on varieties or schemes (quotients)"},"scopeNote":{"en":["See also 13A50, 14L24, 14M17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Lxx","notation":["14Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14L35","notation":["14L35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical groups (algebro-geometric aspects)"},"scopeNote":{"en":["See also 20Gxx, 51N30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Lxx","notation":["14Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14L40","notation":["14L40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other algebraic groups (geometric aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Lxx","notation":["14Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14L99","notation":["14L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Lxx","notation":["14Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M05","notation":["14M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)"},"scopeNote":{"en":["See also 13F15, 13F45, 13H10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M06","notation":["14M06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linkage"},"scopeNote":{"en":["See also 13C40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M07","notation":["14M07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Low codimension problems in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M10","notation":["14M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complete intersections"},"scopeNote":{"en":["See also 13C40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M12","notation":["14M12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Determinantal varieties"},"scopeNote":{"en":["See also 13C40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M15","notation":["14M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Grassmannians, Schubert varieties, flag manifolds"},"scopeNote":{"en":["See also 32M10, 51M35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M17","notation":["14M17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homogeneous spaces and generalizations"},"scopeNote":{"en":["See also 32M10, 53C30, 57T15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M20","notation":["14M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rational and unirational varieties"},"scopeNote":{"en":["See also 14E08"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M22","notation":["14M22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rationally connected varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M25","notation":["14M25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Toric varieties, Newton polyhedra, Okounkov bodies"},"scopeNote":{"en":["See also 52B20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M27","notation":["14M27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compactifications; symmetric and spherical varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M30","notation":["14M30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Supervarieties"},"scopeNote":{"en":["See also 32C11, 58A50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M35","notation":["14M35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Character varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14M99","notation":["14M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Mxx","notation":["14Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Nxx","notation":["14Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Projective and enumerative algebraic geometry"},"scopeNote":{"en":["See also 51-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14N05","notation":["14N05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Projective techniques in algebraic geometry"},"scopeNote":{"en":["See also 51N35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Nxx","notation":["14Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14N07","notation":["14N07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Secant varieties, tensor rank, varieties of sums of powers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Nxx","notation":["14Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14N10","notation":["14N10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Enumerative problems (combinatorial problems) in algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Nxx","notation":["14Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14N15","notation":["14N15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical problems, Schubert calculus"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Nxx","notation":["14Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14N20","notation":["14N20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Configurations and arrangements of linear subspaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Nxx","notation":["14Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14N25","notation":["14N25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Varieties of low degree"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Nxx","notation":["14Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14N30","notation":["14N30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Adjunction problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Nxx","notation":["14Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14N35","notation":["14N35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)"},"scopeNote":{"en":["See also 53D45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Nxx","notation":["14Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14N99","notation":["14N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Nxx","notation":["14Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Pxx","notation":["14Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real algebraic and real-analytic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14P05","notation":["14P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real algebraic sets"},"scopeNote":{"en":["See also 12D15, 13J30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Pxx","notation":["14Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14P10","notation":["14P10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semialgebraic sets and related spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Pxx","notation":["14Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14P15","notation":["14P15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real-analytic and semi-analytic sets"},"scopeNote":{"en":["See also 32B20, 32C05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Pxx","notation":["14Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14P20","notation":["14P20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nash functions and manifolds"},"scopeNote":{"en":["See also 32C07, 58A07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Pxx","notation":["14Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14P25","notation":["14P25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topology of real algebraic varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Pxx","notation":["14Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14P99","notation":["14P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Pxx","notation":["14Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Qxx","notation":["14Qxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational aspects in algebraic geometry"},"scopeNote":{"en":["For software etc., see 14-04; See also 12-08, 13Pxx, 68W30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Q05","notation":["14Q05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational aspects of algebraic curves"},"scopeNote":{"en":["See also 14Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Qxx","notation":["14Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Q10","notation":["14Q10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational aspects of algebraic surfaces"},"scopeNote":{"en":["See also 14Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Qxx","notation":["14Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Q15","notation":["14Q15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational aspects of higher-dimensional varieties"},"scopeNote":{"en":["See also 14Jxx, 14Mxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Qxx","notation":["14Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Q20","notation":["14Q20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Effectivity, complexity and computational aspects of algebraic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Qxx","notation":["14Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Q25","notation":["14Q25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational algebraic geometry over arithmetic ground fields"},"scopeNote":{"en":["See also 14Gxx, 14H25, 14Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Qxx","notation":["14Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Q30","notation":["14Q30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational real algebraic geometry"},"scopeNote":{"en":["See also 14Pxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Qxx","notation":["14Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Q65","notation":["14Q65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric aspects of numerical algebraic geometry"},"scopeNote":{"en":["See also 65H14"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Qxx","notation":["14Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Q99","notation":["14Q99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Qxx","notation":["14Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Rxx","notation":["14Rxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Affine geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14R05","notation":["14R05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classification of affine varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Rxx","notation":["14Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14R10","notation":["14R10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Rxx","notation":["14Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14R15","notation":["14R15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jacobian problem"},"scopeNote":{"en":["See also 13F20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Rxx","notation":["14Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14R20","notation":["14R20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group actions on affine varieties"},"scopeNote":{"en":["See also 13A50, 14L30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Rxx","notation":["14Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14R25","notation":["14R25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Affine fibrations"},"scopeNote":{"en":["See also 14D06"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Rxx","notation":["14Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14R99","notation":["14R99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Rxx","notation":["14Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14Txx","notation":["14Txx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Tropical geometry"},"scopeNote":{"en":["See also 12K10, 14M25, 14N10, 52B20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14-XX","notation":["14-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14T10","notation":["14T10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations of tropical geometry and relations with algebra"},"scopeNote":{"en":["For algebraic aspects, see 15A80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Txx","notation":["14Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14T15","notation":["14T15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial aspects of tropical varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Txx","notation":["14Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14T20","notation":["14T20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric aspects of tropical varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Txx","notation":["14Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14T25","notation":["14T25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic aspects of tropical varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Txx","notation":["14Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14T90","notation":["14T90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of tropical geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Txx","notation":["14Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/14T99","notation":["14T99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/14Txx","notation":["14Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15-XX","notation":["15-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear and multilinear algebra; matrix theory"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/15-01","notation":["15-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15-XX","notation":["15-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15-02","notation":["15-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to linear algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15-XX","notation":["15-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15-03","notation":["15-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of linear algebra"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15-XX","notation":["15-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15-04","notation":["15-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to linear algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15-XX","notation":["15-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15-06","notation":["15-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to linear algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15-XX","notation":["15-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15-11","notation":["15-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to linear algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15-XX","notation":["15-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/15A03","notation":["15A03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vector spaces, linear dependence, rank, lineability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A04","notation":["15A04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear transformations, semilinear transformations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A06","notation":["15A06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear equations (linear algebraic aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A09","notation":["15A09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of matrix inversion and generalized inverses"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A10","notation":["15A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of generalized inverses"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A12","notation":["15A12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Conditioning of matrices"},"scopeNote":{"en":["See also 65F35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A15","notation":["15A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Determinants, permanents, traces, other special matrix functions"},"scopeNote":{"en":["See also 19B10, 19B14"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A16","notation":["15A16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matrix exponential and similar functions of matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A18","notation":["15A18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Eigenvalues, singular values, and eigenvectors"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A20","notation":["15A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Diagonalization, Jordan forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A21","notation":["15A21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Canonical forms, reductions, classification"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A22","notation":["15A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matrix pencils"},"scopeNote":{"en":["See also 47A56"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A23","notation":["15A23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Factorization of matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A24","notation":["15A24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matrix equations and identities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A27","notation":["15A27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutativity of matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A29","notation":["15A29"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems in linear algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A30","notation":["15A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic systems of matrices"},"scopeNote":{"en":["See also 16S50, 20Gxx, 20Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A39","notation":["15A39"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear inequalities of matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A42","notation":["15A42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inequalities involving eigenvalues and eigenvectors"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A45","notation":["15A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Miscellaneous inequalities involving matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A54","notation":["15A54"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matrices over function rings in one or more variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A60","notation":["15A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Norms of matrices, numerical range, applications of functional analysis to matrix theory"},"scopeNote":{"en":["See also 65F35, 65J05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A63","notation":["15A63"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quadratic and bilinear forms, inner products"},"scopeNote":{"en":["See mainly 11Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A66","notation":["15A66"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Clifford algebras, spinors"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A67","notation":["15A67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of Clifford algebras to physics, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A69","notation":["15A69"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multilinear algebra, tensor calculus"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A72","notation":["15A72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vector and tensor algebra, theory of invariants"},"scopeNote":{"en":["See also 13A50, 14L24"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A75","notation":["15A75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exterior algebra, Grassmann algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A78","notation":["15A78"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other algebras built from modules"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A80","notation":["15A80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Max-plus and related algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A83","notation":["15A83"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matrix completion problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A86","notation":["15A86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear preserver problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15A99","notation":["15A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Axx","notation":["15Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15-XX","notation":["15-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B05","notation":["15B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Toeplitz, Cauchy, and related matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B10","notation":["15B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orthogonal matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B15","notation":["15B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B30","notation":["15B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matrix Lie algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B33","notation":["15B33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matrices over special rings (quaternions, finite fields, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B34","notation":["15B34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boolean and Hadamard matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B35","notation":["15B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sign pattern matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B36","notation":["15B36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matrices of integers"},"scopeNote":{"en":["See also 11C20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B48","notation":["15B48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Positive matrices and their generalizations; cones of matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B51","notation":["15B51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B52","notation":["15B52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random matrices (algebraic aspects)"},"scopeNote":{"en":["For probabilistic aspects, see 60B20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B57","notation":["15B57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hermitian, skew-Hermitian, and related matrices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/15B99","notation":["15B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/15Bxx","notation":["15Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Associative rings and algebras"},"scopeNote":{"en":["For the commutative case, see 13-XX"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16-00","notation":["16-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to associative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16-01","notation":["16-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16-02","notation":["16-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to associative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16-03","notation":["16-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of associative rings and algebras"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16-04","notation":["16-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to associative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16-06","notation":["16-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to associative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16-11","notation":["16-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to associative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Bxx","notation":["16Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General and miscellaneous"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16B50","notation":["16B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Category-theoretic methods and results in associative algebras (except as in 16D90)"},"scopeNote":{"en":["See also 18-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Bxx","notation":["16Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16B70","notation":["16B70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of logic in associative algebras"},"scopeNote":{"en":["See also 03Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Bxx","notation":["16Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16B99","notation":["16B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Bxx","notation":["16Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Dxx","notation":["16Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modules, bimodules and ideals in associative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16D10","notation":["16D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General module theory in associative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Dxx","notation":["16Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16D20","notation":["16D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bimodules in associative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Dxx","notation":["16Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16D25","notation":["16D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ideals in associative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Dxx","notation":["16Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16D30","notation":["16D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite-dimensional simple rings (except as in 16Kxx)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Dxx","notation":["16Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16D40","notation":["16D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free, projective, and flat modules and ideals in associative algebras"},"scopeNote":{"en":["See also 19A13"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Dxx","notation":["16Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16D50","notation":["16D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Injective modules, self-injective associative rings"},"scopeNote":{"en":["See also 16L60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Dxx","notation":["16Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16D60","notation":["16D60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Simple and semisimple modules, primitive rings and ideals in associative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Dxx","notation":["16Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16D70","notation":["16D70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Dxx","notation":["16Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16D80","notation":["16D80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other classes of modules and ideals in associative algebras"},"scopeNote":{"en":["See also 16G50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Dxx","notation":["16Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16D90","notation":["16D90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Module categories in associative algebras ; module theory in a category-theoretic context; Morita equivalence and duality"},"scopeNote":{"en":["See also 16Gxx, 16S90"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Dxx","notation":["16Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16D99","notation":["16D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Dxx","notation":["16Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Exx","notation":["16Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological methods in associative algebras"},"scopeNote":{"en":["For commutative rings, see 13Dxx; for general categories, see 18Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16E05","notation":["16E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Syzygies, resolutions, complexes in associative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Exx","notation":["16Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16E10","notation":["16E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological dimension in associative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Exx","notation":["16Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16E20","notation":["16E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Grothendieck groups, K-theory, etc."},"scopeNote":{"en":["See also 18F30, 19Axx, 19D50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Exx","notation":["16Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16E30","notation":["16E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological functors on modules (Tor, Ext, etc.) in associative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Exx","notation":["16Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16E35","notation":["16E35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Derived categories and associative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Exx","notation":["16Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16E40","notation":["16E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Exx","notation":["16Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16E45","notation":["16E45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential graded algebras and applications (associative algebraic aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Exx","notation":["16Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16E50","notation":["16E50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"von Neumann regular rings and generalizations (associative algebraic aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Exx","notation":["16Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16E60","notation":["16E60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Exx","notation":["16Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16E65","notation":["16E65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Exx","notation":["16Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16E99","notation":["16E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Exx","notation":["16Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Gxx","notation":["16Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representation theory of associative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16G10","notation":["16G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of associative Artinian rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Gxx","notation":["16Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16G20","notation":["16G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of quivers and partially ordered sets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Gxx","notation":["16Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16G30","notation":["16G30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of orders, lattices, algebras over commutative rings"},"scopeNote":{"en":["See also 16Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Gxx","notation":["16Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16G50","notation":["16G50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cohen-Macaulay modules in associative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Gxx","notation":["16Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16G60","notation":["16G60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representation type (finite, tame, wild, etc.) of associative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Gxx","notation":["16Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16G70","notation":["16G70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Gxx","notation":["16Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16G99","notation":["16G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Gxx","notation":["16Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Hxx","notation":["16Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Associative algebras and orders"},"scopeNote":{"en":["For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16H05","notation":["16H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Hxx","notation":["16Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16H10","notation":["16H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orders in separable algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Hxx","notation":["16Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16H15","notation":["16H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutative orders"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Hxx","notation":["16Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16H20","notation":["16H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattices over orders"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Hxx","notation":["16Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16H99","notation":["16H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Hxx","notation":["16Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Kxx","notation":["16Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Division rings and semisimple Artin rings"},"scopeNote":{"en":["See also 12E15, 15A30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16K20","notation":["16K20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite-dimensional division rings"},"scopeNote":{"en":["For crossed products, see 16S35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Kxx","notation":["16Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16K40","notation":["16K40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite-dimensional and general division rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Kxx","notation":["16Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16K50","notation":["16K50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Brauer groups (algebraic aspects)"},"scopeNote":{"en":["See also 12G05, 14F22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Kxx","notation":["16Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16K99","notation":["16K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Kxx","notation":["16Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Lxx","notation":["16Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local rings and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16L30","notation":["16L30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative local and semilocal rings, perfect rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Lxx","notation":["16Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16L60","notation":["16L60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasi-Frobenius rings"},"scopeNote":{"en":["See also 16D50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Lxx","notation":["16Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16L99","notation":["16L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Lxx","notation":["16Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Nxx","notation":["16Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Radicals and radical properties of associative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16N20","notation":["16N20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jacobson radical, quasimultiplication"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Nxx","notation":["16Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16N40","notation":["16N40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nil and nilpotent radicals, sets, ideals, associative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Nxx","notation":["16Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16N60","notation":["16N60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Prime and semiprime associative rings"},"scopeNote":{"en":["See also 16D60, 16U10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Nxx","notation":["16Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16N80","notation":["16N80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General radicals and associative rings"},"scopeNote":{"en":["For radicals in module categories, see 16S90"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Nxx","notation":["16Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16N99","notation":["16N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Nxx","notation":["16Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Pxx","notation":["16Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16P10","notation":["16P10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite rings and finite-dimensional associative algebras"},"scopeNote":{"en":["For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Pxx","notation":["16Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16P20","notation":["16P20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Artinian rings and modules (associative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Pxx","notation":["16Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16P40","notation":["16P40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noetherian rings and modules (associative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Pxx","notation":["16Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16P50","notation":["16P50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Localization and associative Noetherian rings"},"scopeNote":{"en":["See also 16U20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Pxx","notation":["16Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16P60","notation":["16P60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chain conditions on annihilators and summands: Goldie-type conditions , Krull dimension (associative rings and algebras)"},"scopeNote":{"en":["See also 16U20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Pxx","notation":["16Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16P70","notation":["16P70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Pxx","notation":["16Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16P90","notation":["16P90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Growth rate, Gelfand-Kirillov dimension"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Pxx","notation":["16Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16P99","notation":["16P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Pxx","notation":["16Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Rxx","notation":["16Rxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rings with polynomial identity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16R10","notation":["16R10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"T -ideals, identities, varieties of associative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Rxx","notation":["16Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16R20","notation":["16R20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semiprime p.i. rings, rings embeddable in matrices over commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Rxx","notation":["16Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16R30","notation":["16R30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Trace rings and invariant theory (associative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Rxx","notation":["16Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16R40","notation":["16R40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Identities other than those of matrices over commutative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Rxx","notation":["16Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16R50","notation":["16R50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other kinds of identities (generalized polynomial, rational, involution)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Rxx","notation":["16Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16R60","notation":["16R60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional identities (associative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Rxx","notation":["16Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16R99","notation":["16R99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Rxx","notation":["16Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Associative rings and algebras arising under various constructions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S10","notation":["16S10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S15","notation":["16S15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S20","notation":["16S20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Centralizing and normalizing extensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S30","notation":["16S30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Universal enveloping algebras of Lie algebras"},"scopeNote":{"en":["See mainly 17B35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S32","notation":["16S32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rings of differential operators (associative algebraic aspects)"},"scopeNote":{"en":["See also 13N10, 32C38"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S34","notation":["16S34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group rings , Laurent polynomial rings (associative algebraic aspects)"},"scopeNote":{"en":["See also 20C05, 20C07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S35","notation":["16S35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Twisted and skew group rings, crossed products"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S36","notation":["16S36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary and skew polynomial rings and semigroup rings"},"scopeNote":{"en":["See also 20M25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S37","notation":["16S37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quadratic and Koszul algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S38","notation":["16S38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rings arising from noncommutative algebraic geometry"},"scopeNote":{"en":["See also 14A22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S40","notation":["16S40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Smash products of general Hopf actions"},"scopeNote":{"en":["See also 16T05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S50","notation":["16S50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Endomorphism rings; matrix rings"},"scopeNote":{"en":["See also 15-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S60","notation":["16S60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Associative rings of functions, subdirect products, sheaves of rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S70","notation":["16S70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extensions of associative rings by ideals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S80","notation":["16S80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deformations of associative rings"},"scopeNote":{"en":["See also 13D10, 14D15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S85","notation":["16S85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Associative rings of fractions and localizations"},"scopeNote":{"en":["See also 13B30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S88","notation":["16S88"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Leavitt path algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S90","notation":["16S90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Torsion theories; radicals on module categories (associative algebraic aspects)"},"scopeNote":{"en":["See also 13D30, 18E40; For radicals of rings, see 16Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16S99","notation":["16S99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Sxx","notation":["16Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Txx","notation":["16Txx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hopf algebras, quantum groups and related topics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16T05","notation":["16T05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hopf algebras and their applications"},"scopeNote":{"en":["See also 16S40, 57T05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Txx","notation":["16Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16T10","notation":["16T10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bialgebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Txx","notation":["16Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16T15","notation":["16T15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Coalgebras and comodules; corings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Txx","notation":["16Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16T20","notation":["16T20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ring-theoretic aspects of quantum groups"},"scopeNote":{"en":["See also 17B37, 20G42, 81R50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Txx","notation":["16Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16T25","notation":["16T25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Yang-Baxter equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Txx","notation":["16Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16T30","notation":["16T30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connections of associative rings and algebras with combinatorics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Txx","notation":["16Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16T99","notation":["16T99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Txx","notation":["16Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Uxx","notation":["16Uxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Conditions on elements"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16U10","notation":["16U10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral domains (associative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Uxx","notation":["16Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16U20","notation":["16U20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ore rings, multiplicative sets, Ore localization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Uxx","notation":["16Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16U30","notation":["16U30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Divisibility, noncommutative UFDs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Uxx","notation":["16Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16U40","notation":["16U40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Idempotent elements"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Uxx","notation":["16Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16U50","notation":["16U50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized inverses"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Uxx","notation":["16Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16U60","notation":["16U60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Units, groups of units (associative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Uxx","notation":["16Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16U70","notation":["16U70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Center, normalizer (invariant elements) (associative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Uxx","notation":["16Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16U80","notation":["16U80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of commutativity (associative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Uxx","notation":["16Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16U99","notation":["16U99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Uxx","notation":["16Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Wxx","notation":["16Wxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Associative rings and algebras with additional structure"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16W10","notation":["16W10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rings with involution; Lie, Jordan and other nonassociative structures"},"scopeNote":{"en":["See also 17B60, 17C50, 46Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Wxx","notation":["16Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16W20","notation":["16W20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphisms and endomorphisms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Wxx","notation":["16Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16W22","notation":["16W22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Actions of groups and semigroups; invariant theory (associative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Wxx","notation":["16Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16W25","notation":["16W25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Derivations, actions of Lie algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Wxx","notation":["16Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16W50","notation":["16W50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graded rings and modules (associative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Wxx","notation":["16Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16W55","notation":["16W55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"“Super” (or “skew”) structure"},"scopeNote":{"en":["See also 17A70, 17Bxx, 17C70; For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Wxx","notation":["16Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16W60","notation":["16W60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Valuations, completions, formal power series and related constructions (associative rings and algebras)"},"scopeNote":{"en":["See also 13Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Wxx","notation":["16Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16W70","notation":["16W70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Filtered associative rings; filtrational and graded techniques"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Wxx","notation":["16Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16W80","notation":["16W80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological and ordered rings and modules"},"scopeNote":{"en":["See also 06F25, 13Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Wxx","notation":["16Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16W99","notation":["16W99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Wxx","notation":["16Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Yxx","notation":["16Yxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations"},"scopeNote":{"en":["For nonassociative rings, see 17-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Y20","notation":["16Y20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperrings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Yxx","notation":["16Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Y30","notation":["16Y30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Near-rings"},"scopeNote":{"en":["See also 12K05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Yxx","notation":["16Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Y60","notation":["16Y60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semirings"},"scopeNote":{"en":["See also 12K10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Yxx","notation":["16Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Y80","notation":["16Y80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Γ and fuzzy structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Yxx","notation":["16Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Y99","notation":["16Y99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Yxx","notation":["16Yxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Zxx","notation":["16Zxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational aspects of associative rings"},"scopeNote":{"en":["For software etc., see 16-04"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16-XX","notation":["16-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Z05","notation":["16Z05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational aspects of associative rings"},"scopeNote":{"en":["See also 68W30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Zxx","notation":["16Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Z10","notation":["16Z10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gröbner-Shirshov bases"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Zxx","notation":["16Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/16Z99","notation":["16Z99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/16Zxx","notation":["16Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonassociative rings and algebras"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17-00","notation":["17-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to nonassociative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17-01","notation":["17-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to nonassociative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17-02","notation":["17-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17-03","notation":["17-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of nonassociative rings and algebras"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17-04","notation":["17-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to nonassociative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17-06","notation":["17-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to nonassociative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17-08","notation":["17-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to nonassociative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17-11","notation":["17-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to nonassociative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General nonassociative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A01","notation":["17A01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of nonassociative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A05","notation":["17A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Power-associative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A15","notation":["17A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative Jordan algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A20","notation":["17A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Flexible algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A30","notation":["17A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonassociative algebras satisfying other identities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A32","notation":["17A32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Leibniz algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A35","notation":["17A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonassociative division algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A36","notation":["17A36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphisms, derivations, other operators (nonassociative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A40","notation":["17A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ternary compositions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A42","notation":["17A42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other n-ary compositions (n ≥ 3)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A45","notation":["17A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quadratic algebras (but not quadratic Jordan algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A50","notation":["17A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free nonassociative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A60","notation":["17A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure theory for nonassociative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A61","notation":["17A61"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gröbner-Shirshov bases in nonassociative algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A65","notation":["17A65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Radical theory (nonassociative rings and algebras)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A70","notation":["17A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Superalgebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A75","notation":["17A75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Composition algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A80","notation":["17A80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Valued algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17A99","notation":["17A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Axx","notation":["17Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lie algebras and Lie superalgebras"},"scopeNote":{"en":["For Lie groups, see 22Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B01","notation":["17B01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Identities, free Lie (super)algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B05","notation":["17B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure theory for Lie algebras and superalgebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B08","notation":["17B08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Coadjoint orbits; nilpotent varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B10","notation":["17B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B15","notation":["17B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of Lie algebras and Lie superalgebras, analytic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B20","notation":["17B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Simple, semisimple, reductive (super)algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B22","notation":["17B22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Root systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B25","notation":["17B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exceptional (super)algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B30","notation":["17B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Solvable, nilpotent (super)algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B35","notation":["17B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Universal enveloping (super)algebras"},"scopeNote":{"en":["See also 16S30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B37","notation":["17B37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum groups (quantized enveloping algebras) and related deformations"},"scopeNote":{"en":["See also 16T20, 20G42, 81R50, 82B23"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B38","notation":["17B38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Yang-Baxter equations and Rota-Baxter operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B40","notation":["17B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphisms, derivations, other operators for Lie algebras and super algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B45","notation":["17B45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lie algebras of linear algebraic groups"},"scopeNote":{"en":["See also 14Lxx and 20Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B50","notation":["17B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modular Lie (super)algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B55","notation":["17B55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological methods in Lie (super)algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B56","notation":["17B56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cohomology of Lie (super)algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B60","notation":["17B60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lie (super)algebras associated with other structures (associative, Jordan, etc.)"},"scopeNote":{"en":["See also 16W10, 17C40, 17C50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B61","notation":["17B61"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hom-Lie and related algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B62","notation":["17B62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lie bialgebras; Lie coalgebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B63","notation":["17B63"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Poisson algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B65","notation":["17B65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite-dimensional Lie (super)algebras"},"scopeNote":{"en":["See also 22E65"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B66","notation":["17B66"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lie algebras of vector fields and related (super) algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B67","notation":["17B67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B68","notation":["17B68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Virasoro and related algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B69","notation":["17B69"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vertex operators; vertex operator algebras and related structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B70","notation":["17B70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graded Lie (super)algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B75","notation":["17B75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Color Lie (super)algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B80","notation":["17B80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of Lie algebras and superalgebras to integrable systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B81","notation":["17B81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of Lie (super)algebras to physics, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17B99","notation":["17B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Bxx","notation":["17Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jordan algebras (algebras, triples and pairs)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C05","notation":["17C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Identities and free Jordan structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C10","notation":["17C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure theory for Jordan algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C17","notation":["17C17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Radicals in Jordan algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C20","notation":["17C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Simple, semisimple Jordan algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C27","notation":["17C27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Idempotents, Peirce decompositions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C30","notation":["17C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Associated groups, automorphisms of Jordan algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C36","notation":["17C36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Associated manifolds of Jordan algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C37","notation":["17C37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Associated geometries of Jordan algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C40","notation":["17C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exceptional Jordan structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C50","notation":["17C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jordan structures associated with other structures"},"scopeNote":{"en":["See also 16W10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C55","notation":["17C55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite-dimensional structures of Jordan algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C60","notation":["17C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Division algebras and Jordan algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C65","notation":["17C65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jordan structures on Banach spaces and algebras"},"scopeNote":{"en":["See also 46H70, 46L70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C70","notation":["17C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Super structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C90","notation":["17C90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of Jordan algebras to physics, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17C99","notation":["17C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Cxx","notation":["17Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17Dxx","notation":["17Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other nonassociative rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17-XX","notation":["17-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17D05","notation":["17D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Alternative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Dxx","notation":["17Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17D10","notation":["17D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mal’tsev rings and algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Dxx","notation":["17Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17D15","notation":["17D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Right alternative rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Dxx","notation":["17Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17D20","notation":["17D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"(γ, δ)-rings, including (1, −1)-rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Dxx","notation":["17Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17D25","notation":["17D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lie-admissible algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Dxx","notation":["17Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17D30","notation":["17D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"(non-Lie) Hom algebras and topics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Dxx","notation":["17Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17D92","notation":["17D92"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Genetic algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Dxx","notation":["17Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/17D99","notation":["17D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/17Dxx","notation":["17Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Category theory; homological algebra"},"scopeNote":{"en":["For commutative rings, see 13Dxx; for associative rings, see 16Exx; for groups, see 20Jxx; for topological groups and related structures, see 57Txx; for algebraic topology, see also 55Nxx, 55Uxx"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18-00","notation":["18-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to category theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18-01","notation":["18-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to category theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18-02","notation":["18-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to category theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18-03","notation":["18-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of category theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18-04","notation":["18-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to category theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18-06","notation":["18-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to category theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18-08","notation":["18-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to category theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18-11","notation":["18-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to category theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of categories and functors"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A05","notation":["18A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Definitions and generalizations in theory of categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A10","notation":["18A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graphs, diagram schemes, precategories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A15","notation":["18A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations, relations to logic and deductive systems"},"scopeNote":{"en":["See also 03-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A20","notation":["18A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Epimorphisms, monomorphisms, special classes of morphisms, null morphisms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A22","notation":["18A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special properties of functors (faithful, full, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A23","notation":["18A23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Natural morphisms, dinatural morphisms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A25","notation":["18A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functor categories, comma categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A30","notation":["18A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A32","notation":["18A32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Factorization systems, substructures, quotient structures, congruences, amalgams"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A35","notation":["18A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categories admitting limits (complete categories), functors preserving limits, completions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A40","notation":["18A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A50","notation":["18A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graded categories (general)"},"scopeNote":{"en":["For dg categories, see 18G35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18A99","notation":["18A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Axx","notation":["18Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18Bxx","notation":["18Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18B05","notation":["18B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categories of sets, characterizations"},"scopeNote":{"en":["See also 03-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Bxx","notation":["18Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18B10","notation":["18B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categories of spans/cospans, relations, or partial maps"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Bxx","notation":["18Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18B15","notation":["18B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Embedding theorems, universal categories"},"scopeNote":{"en":["See also 18E20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Bxx","notation":["18Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18B20","notation":["18B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categories of machines, automata"},"scopeNote":{"en":["See also 03D05, 68Qxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Bxx","notation":["18Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18B25","notation":["18B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topoi"},"scopeNote":{"en":["See also 03G30, 18F10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Bxx","notation":["18Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18B35","notation":["18B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Preorders, orders, domains and lattices (viewed as categories)"},"scopeNote":{"en":["See also 06-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Bxx","notation":["18Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18B40","notation":["18B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groupoids, semigroupoids, semigroups, groups (viewed as categories)"},"scopeNote":{"en":["See also 20Axx, 20L05, 20Mxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Bxx","notation":["18Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18B50","notation":["18B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extensive, distributive, and adhesive categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Bxx","notation":["18Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18B99","notation":["18B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Bxx","notation":["18Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18Cxx","notation":["18Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categories and theories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18C05","notation":["18C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equational categories"},"scopeNote":{"en":["See also 03C05, 08C05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Cxx","notation":["18Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18C10","notation":["18C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theories (e.g., algebraic theories), structure, and semantics"},"scopeNote":{"en":["See also 03G30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Cxx","notation":["18Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18C15","notation":["18C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monads (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples"},"scopeNote":{"en":["See also 18Gxx; For functional programming, see also 68N18"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Cxx","notation":["18Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18C20","notation":["18C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Eilenberg-Moore and Kleisli constructions for monads"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Cxx","notation":["18Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18C30","notation":["18C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sketches and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Cxx","notation":["18Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18C35","notation":["18C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Accessible and locally presentable categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Cxx","notation":["18Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18C40","notation":["18C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structured objects in a category (group objects, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Cxx","notation":["18Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18C50","notation":["18C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categorical semantics of formal languages"},"scopeNote":{"en":["See also 68Q55, 68Q65"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Cxx","notation":["18Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18C99","notation":["18C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Cxx","notation":["18Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18Dxx","notation":["18Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categorical structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18D15","notation":["18D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Closed categories (closed monoidal and Cartesian closed categories, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Dxx","notation":["18Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18D20","notation":["18D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Enriched categories (over closed or monoidal categories)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Dxx","notation":["18Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18D25","notation":["18D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Actions of a monoidal category, tensorial strength"},"scopeNote":{"en":["For functional programming, see also 68N18"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Dxx","notation":["18Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18D30","notation":["18D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fibered categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Dxx","notation":["18Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18D40","notation":["18D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Internal categories and groupoids"},"scopeNote":{"en":["For double categories, see 18N10; for topological groupoids, see 22A22; for Lie groupoids, see 58H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Dxx","notation":["18Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18D60","notation":["18D60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Profunctors (= correspondences, distributors, modules)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Dxx","notation":["18Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18D65","notation":["18D65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proarrow equipments, Yoneda structures, KZ doctrines (lax idempotent monads)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Dxx","notation":["18Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18D70","notation":["18D70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Formal category theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Dxx","notation":["18Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18D99","notation":["18D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Dxx","notation":["18Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18Exx","notation":["18Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categorical algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18E05","notation":["18E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Preadditive, additive categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Exx","notation":["18Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18E08","notation":["18E08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Regular categories, Barr-exact categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Exx","notation":["18Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18E10","notation":["18E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abelian categories, Grothendieck categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Exx","notation":["18Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18E13","notation":["18E13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Protomodular categories, semi-abelian categories, Mal’tsev categories"},"scopeNote":{"en":["See also 08B05 and 18B10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Exx","notation":["18Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18E20","notation":["18E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categorical embedding theorems"},"scopeNote":{"en":["See also 18B15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Exx","notation":["18Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18E35","notation":["18E35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Localization of categories, calculus of fractions"},"scopeNote":{"en":["For homotopical aspects, see also 18N45, 55P60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Exx","notation":["18Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18E40","notation":["18E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Torsion theories, radicals"},"scopeNote":{"en":["See also 13D30, 16S90"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Exx","notation":["18Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18E45","notation":["18E45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Definable subcategories and connections with model theory"},"scopeNote":{"en":["See also 13C60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Exx","notation":["18Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18E50","notation":["18E50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categorical Galois theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Exx","notation":["18Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18E99","notation":["18E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Exx","notation":["18Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categories in geometry and topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18F05","notation":["18F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local categories and functors"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18F10","notation":["18F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Grothendieck topologies and Grothendieck topoi"},"scopeNote":{"en":["See also 14F20, 18B25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18F15","notation":["18F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract manifolds and fiber bundles (category-theoretic aspects)"},"scopeNote":{"en":["See also 55Rxx, 57Pxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18F20","notation":["18F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)"},"scopeNote":{"en":["See also 14F06, 14F07, 32C35, 32L10, 54B40, 55N30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18F25","notation":["18F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic K-theory and L-theory (category-theoretic aspects)"},"scopeNote":{"en":["See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18F30","notation":["18F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Grothendieck groups (category-theoretic aspects)"},"scopeNote":{"en":["See also 13D15, 16E20, 19Axx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18F40","notation":["18F40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Synthetic differential geometry, tangent categories, differential categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18F50","notation":["18F50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Goodwillie calculus and functor calculus"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18F60","notation":["18F60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categories of topological spaces and continuous mappings"},"scopeNote":{"en":["See also 54-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18F70","notation":["18F70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Frames and locales, pointfree topology, Stone duality"},"scopeNote":{"en":["See also 06D22, 18B35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18F75","notation":["18F75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantales"},"scopeNote":{"en":["See also 06F07, 18B35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18F99","notation":["18F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Fxx","notation":["18Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological algebra in category theory, derived categories and functors"},"scopeNote":{"en":["See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G05","notation":["18G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Projectives and injectives (category-theoretic aspects)"},"scopeNote":{"en":["See also 13C10, 13C11, 16D40, 16D50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G10","notation":["18G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Resolutions; derived functors (category-theoretic aspects)"},"scopeNote":{"en":["See also 13D02, 16E05, 18Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G15","notation":["18G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)"},"scopeNote":{"en":["See also 55U25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G20","notation":["18G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological dimension (category-theoretic aspects)"},"scopeNote":{"en":["See also 13D05, 16E10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G25","notation":["18G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relative homological algebra, projective classes (category-theoretic aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G31","notation":["18G31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Simplicial modules and Dold-Kan correspondence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G35","notation":["18G35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chain complexes (category-theoretic aspects), dg categories"},"scopeNote":{"en":["See also 14F07, 18G80, 55U15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G40","notation":["18G40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral sequences, hypercohomology"},"scopeNote":{"en":["See also 55Txx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G45","notation":["18G45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"2-groups, crossed modules, crossed complexes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G50","notation":["18G50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonabelian homological algebra (category-theoretic aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G65","notation":["18G65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stable module categories"},"scopeNote":{"en":["See also 20C20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G70","notation":["18G70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"A∞ -categories, relations with homological mirror symmetry"},"scopeNote":{"en":["See also 14F07, 14J33, 53D37"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G80","notation":["18G80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Derived categories, triangulated categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G85","notation":["18G85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graph complexes and graph homology"},"scopeNote":{"en":["For relations with deformation quantization, see 53D55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G90","notation":["18G90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other (co)homology theories (category-theoretic aspects)"},"scopeNote":{"en":["See also 19D55, 46L80, 58J20, 58J22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18G99","notation":["18G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Gxx","notation":["18Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monoidal categories and operads"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M05","notation":["18M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monoidal categories, symmetric monoidal categories"},"scopeNote":{"en":["See also 19D23"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M10","notation":["18M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Traced monoidal categories, compact closed categories, star-autonomous categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M15","notation":["18M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Braided monoidal categories and ribbon categories"},"scopeNote":{"en":["For applications to knot theory, see also 57Kxx; for applications to quantum groups, see also 16T20, 17B37, 81R50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M20","notation":["18M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fusion categories, modular tensor categories, modular functors"},"scopeNote":{"en":["For applications to topological quantum field theories, see also 57R56; for applications to conformal field theories, see also 81T40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M25","notation":["18M25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Tannakian categories"},"scopeNote":{"en":["For applications to motives, see also 14C15, 19E15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M30","notation":["18M30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"String diagrams and graphical calculi"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M35","notation":["18M35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categories of networks and processes, compositionality"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M40","notation":["18M40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dagger categories, categorical quantum mechanics"},"scopeNote":{"en":["See also 81P68"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M45","notation":["18M45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categorical aspects of linear logic"},"scopeNote":{"en":["See also 03B47"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M50","notation":["18M50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bimonoidal, skew-monoidal, duoidal categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M60","notation":["18M60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operads (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M65","notation":["18M65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Non-symmetric operads, multicategories, generalized multicategories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M70","notation":["18M70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic operads, cooperads, and Koszul duality"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M75","notation":["18M75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological and simplicial operads"},"scopeNote":{"en":["See also 18N60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M80","notation":["18M80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Species, Hopf monoids, operads in combinatorics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M85","notation":["18M85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polycategories/dioperads, properads, PROPs, cyclic operads, modular operads"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M90","notation":["18M90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Globular operads"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18M99","notation":["18M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Mxx","notation":["18Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher categories and homotopical algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18-XX","notation":["18-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N10","notation":["18N10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"2-categories, bicategories, double categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N15","notation":["18N15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"2-dimensional monad theory"},"scopeNote":{"en":["See also 18C15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N20","notation":["18N20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Tricategories, weak n-categories, coherence, semi-strictification"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N25","notation":["18N25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categorification"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N30","notation":["18N30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Strict omega-categories, computads, polygraphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N40","notation":["18N40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homotopical algebra, Quillen model categories, derivators"},"scopeNote":{"en":["See also 55U35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N45","notation":["18N45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categories of fibrations, relations to K-theory, relations to type theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N50","notation":["18N50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Simplicial sets, simplicial objects"},"scopeNote":{"en":["See also 55U10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N55","notation":["18N55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Localizations (e.g., simplicial localization, Bousfield localization)"},"scopeNote":{"en":["See also 18E35, 55P60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N60","notation":["18N60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"(∞, 1)-categories (quasi-categories, Segal spaces, etc.); ∞-topoi, stable ∞-categories"},"scopeNote":{"en":["See also 55U35, 55U40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N65","notation":["18N65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"(∞, n)-categories and (∞, ∞)-categories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N70","notation":["18N70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"∞-operads and higher algebra"},"scopeNote":{"en":["See also 18M75"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/18N99","notation":["18N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/18Nxx","notation":["18Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K-theory"},"scopeNote":{"en":["See also 16E20, 18F25"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19-00","notation":["19-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19-01","notation":["19-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19-02","notation":["19-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19-03","notation":["19-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of K-theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19-04","notation":["19-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19-06","notation":["19-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19-08","notation":["19-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19-11","notation":["19-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19Axx","notation":["19Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Grothendieck groups and K0"},"scopeNote":{"en":["See also 13D15, 18F30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19A13","notation":["19A13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability for projective modules"},"scopeNote":{"en":["See also 13C10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Axx","notation":["19Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19A15","notation":["19A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Efficient generation of modules"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Axx","notation":["19Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19A22","notation":["19A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Frobenius induction, Burnside and representation rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Axx","notation":["19Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19A31","notation":["19A31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K0 of group rings and orders"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Axx","notation":["19Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19A49","notation":["19A49"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K0 of other rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Axx","notation":["19Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19A99","notation":["19A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Axx","notation":["19Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19Bxx","notation":["19Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Whitehead groups and K1"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19B10","notation":["19B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stable range conditions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Bxx","notation":["19Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19B14","notation":["19B14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability for linear groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Bxx","notation":["19Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19B28","notation":["19B28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K1 of group rings and orders"},"scopeNote":{"en":["See also 57Q10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Bxx","notation":["19Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19B37","notation":["19B37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Congruence subgroup problems"},"scopeNote":{"en":["See also 20H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Bxx","notation":["19Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19B99","notation":["19B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Bxx","notation":["19Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19Cxx","notation":["19Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Steinberg groups and K2"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19C09","notation":["19C09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Central extensions and Schur multipliers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Cxx","notation":["19Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19C20","notation":["19C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symbols, presentations and stability of K2"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Cxx","notation":["19Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19C30","notation":["19C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K2 and the Brauer group"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Cxx","notation":["19Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19C40","notation":["19C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Excision for K2"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Cxx","notation":["19Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19C99","notation":["19C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Cxx","notation":["19Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19Dxx","notation":["19Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher algebraic K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19D06","notation":["19D06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Q- and plus-constructions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Dxx","notation":["19Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19D10","notation":["19D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic K-theory of spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Dxx","notation":["19Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19D23","notation":["19D23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symmetric monoidal categories"},"scopeNote":{"en":["See also 18M05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Dxx","notation":["19Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19D25","notation":["19D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Karoubi-Villamayor-Gersten K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Dxx","notation":["19Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19D35","notation":["19D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Negative K-theory, NK and Nil"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Dxx","notation":["19Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19D45","notation":["19D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher symbols, Milnor K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Dxx","notation":["19Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19D50","notation":["19D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computations of higher K-theory of rings"},"scopeNote":{"en":["See also 13D15, 16E20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Dxx","notation":["19Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19D55","notation":["19D55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K-theory and homology; cyclic homology and cohomology"},"scopeNote":{"en":["See also 18G90"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Dxx","notation":["19Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19D99","notation":["19D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Dxx","notation":["19Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19Exx","notation":["19Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K-theory in geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19E08","notation":["19E08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K-theory of schemes"},"scopeNote":{"en":["See also 14C35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Exx","notation":["19Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19E15","notation":["19E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic cycles and motivic cohomology (K-theoretic aspects)"},"scopeNote":{"en":["See also 14C25, 14C35, 14F42"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Exx","notation":["19Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19E20","notation":["19E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations of K-theory with cohomology theories"},"scopeNote":{"en":["See also 14Fxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Exx","notation":["19Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19E99","notation":["19E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Exx","notation":["19Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19Fxx","notation":["19Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K-theory in number theory"},"scopeNote":{"en":["See also 11R70, 11S70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19F05","notation":["19F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized class field theory (K-theoretic aspects)"},"scopeNote":{"en":["See also 11G45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Fxx","notation":["19Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19F15","notation":["19F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symbols and arithmetic (K-theoretic aspects)"},"scopeNote":{"en":["See also 11R37"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Fxx","notation":["19Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19F27","notation":["19F27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Étale cohomology, higher regulators, zeta and L-functions (K-theoretic aspects)"},"scopeNote":{"en":["See also 11G40, 11R42, 11S40, 14F20, 14G10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Fxx","notation":["19Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19F99","notation":["19F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Fxx","notation":["19Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19Gxx","notation":["19Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K-theory of forms"},"scopeNote":{"en":["See also 11Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19G05","notation":["19G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability for quadratic modules"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Gxx","notation":["19Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19G12","notation":["19G12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Witt groups of rings"},"scopeNote":{"en":["See also 11E81"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Gxx","notation":["19Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19G24","notation":["19G24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"L-theory of group rings"},"scopeNote":{"en":["See also 11E81"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Gxx","notation":["19Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19G38","notation":["19G38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hermitian K-theory, relations with K-theory of rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Gxx","notation":["19Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19G99","notation":["19G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Gxx","notation":["19Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19Jxx","notation":["19Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Obstructions from topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19J05","notation":["19J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finiteness and other obstructions in K0"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Jxx","notation":["19Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19J10","notation":["19J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Whitehead (and related) torsion"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Jxx","notation":["19Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19J25","notation":["19J25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Surgery obstructions (K-theoretic aspects)"},"scopeNote":{"en":["See also 57R67"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Jxx","notation":["19Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19J35","notation":["19J35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Obstructions to group actions (K-theoretic aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Jxx","notation":["19Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19J99","notation":["19J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Jxx","notation":["19Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19Kxx","notation":["19Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K-theory and operator algebras"},"scopeNote":{"en":["See mainly 46L80, and also 46M20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19K14","notation":["19K14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K0 as an ordered group, traces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Kxx","notation":["19Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19K33","notation":["19K33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ext and K-homology"},"scopeNote":{"en":["See also 55N22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Kxx","notation":["19Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19K35","notation":["19K35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kasparov theory (KK-theory)"},"scopeNote":{"en":["See also 58J22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Kxx","notation":["19Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19K56","notation":["19K56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Index theory"},"scopeNote":{"en":["See also 58J20, 58J22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Kxx","notation":["19Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19K99","notation":["19K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Kxx","notation":["19Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19Lxx","notation":["19Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological K-theory"},"scopeNote":{"en":["See also 55N15, 55R50, 55S25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19L10","notation":["19L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Riemann-Roch theorems, Chern characters"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Lxx","notation":["19Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19L20","notation":["19L20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"J-homomorphism, Adams operations"},"scopeNote":{"en":["See also 55Q50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Lxx","notation":["19Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19L41","notation":["19L41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connective K-theory, cobordism"},"scopeNote":{"en":["See also 55N22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Lxx","notation":["19Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19L47","notation":["19L47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equivariant K-theory"},"scopeNote":{"en":["See also 55N91, 55P91, 55Q91, 55R91, 55S91"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Lxx","notation":["19Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19L50","notation":["19L50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Twisted K-theory; differential K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Lxx","notation":["19Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19L64","notation":["19L64"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric applications of topological K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Lxx","notation":["19Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19L99","notation":["19L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Lxx","notation":["19Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19Mxx","notation":["19Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Miscellaneous applications of K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19-XX","notation":["19-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19M05","notation":["19M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Miscellaneous applications of K-theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Mxx","notation":["19Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/19M99","notation":["19M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/19Mxx","notation":["19Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group theory and generalizations"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20-00","notation":["20-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to group theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20-01","notation":["20-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20-02","notation":["20-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to group theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20-03","notation":["20-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of group theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20-04","notation":["20-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to group theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20-06","notation":["20-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to group theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20-08","notation":["20-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to group theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20-11","notation":["20-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to group theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Axx","notation":["20Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20A05","notation":["20A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axiomatics and elementary properties of groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Axx","notation":["20Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20A10","notation":["20A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Metamathematical considerations in group theory"},"scopeNote":{"en":["For word problems, see 20F10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Axx","notation":["20Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20A15","notation":["20A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of logic to group theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Axx","notation":["20Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20A99","notation":["20A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Axx","notation":["20Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Bxx","notation":["20Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Permutation groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20B05","notation":["20B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory for finite permutation groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Bxx","notation":["20Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20B07","notation":["20B07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory for infinite permutation groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Bxx","notation":["20Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20B10","notation":["20B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Characterization theorems for permutation groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Bxx","notation":["20Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20B15","notation":["20B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Primitive groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Bxx","notation":["20Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20B20","notation":["20B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiply transitive finite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Bxx","notation":["20Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20B22","notation":["20B22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiply transitive infinite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Bxx","notation":["20Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20B25","notation":["20B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite automorphism groups of algebraic, geometric, or combinatorial structures"},"scopeNote":{"en":["See also 05Bxx, 12F10, 20G40, 20H30, 51-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Bxx","notation":["20Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20B27","notation":["20B27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite automorphism groups"},"scopeNote":{"en":["See also 12F10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Bxx","notation":["20Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20B30","notation":["20B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symmetric groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Bxx","notation":["20Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20B35","notation":["20B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subgroups of symmetric groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Bxx","notation":["20Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20B99","notation":["20B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Bxx","notation":["20Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representation theory of groups"},"scopeNote":{"en":["For representation rings and Burnside rings, see also 19A22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C05","notation":["20C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group rings of finite groups and their modules (group-theoretic aspects)"},"scopeNote":{"en":["See also 16S34"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C07","notation":["20C07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group rings of infinite groups and their modules (group-theoretic aspects)"},"scopeNote":{"en":["See also 16S34"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C08","notation":["20C08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hecke algebras and their representations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C10","notation":["20C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral representations of finite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C11","notation":["20C11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"p-adic representations of finite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C12","notation":["20C12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral representations of infinite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C15","notation":["20C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary representations and characters"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C20","notation":["20C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modular representations and characters"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C25","notation":["20C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Projective representations and multipliers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C30","notation":["20C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of finite symmetric groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C32","notation":["20C32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of infinite symmetric groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C33","notation":["20C33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of finite groups of Lie type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C34","notation":["20C34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of sporadic groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C35","notation":["20C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of group representations to physics and other areas of science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20C99","notation":["20C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Cxx","notation":["20Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract finite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D05","notation":["20D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite simple groups and their classification"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D06","notation":["20D06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Simple groups: alternating groups and groups of Lie type"},"scopeNote":{"en":["See also 20Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D08","notation":["20D08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Simple groups: sporadic groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D10","notation":["20D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks"},"scopeNote":{"en":["See also 20F17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D15","notation":["20D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite nilpotent groups, p-groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D20","notation":["20D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sylow subgroups, Sylow properties, π-groups, π-structure"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D25","notation":["20D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special subgroups (Frattini, Fitting, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D30","notation":["20D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Series and lattices of subgroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D35","notation":["20D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subnormal subgroups of abstract finite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D40","notation":["20D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Products of subgroups of abstract finite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D45","notation":["20D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphisms of abstract finite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D60","notation":["20D60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic and combinatorial problems involving abstract finite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20D99","notation":["20D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Dxx","notation":["20Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure and classification of infinite or finite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E05","notation":["20E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free nonabelian groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E06","notation":["20E06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E07","notation":["20E07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subgroup theorems; subgroup growth"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E08","notation":["20E08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groups acting on trees"},"scopeNote":{"en":["See also 20F65"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E10","notation":["20E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasivarieties and varieties of groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E15","notation":["20E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chains and lattices of subgroups, subnormal subgroups"},"scopeNote":{"en":["See also 20F22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E18","notation":["20E18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Limits, profinite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E22","notation":["20E22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extensions, wreath products, and other compositions of groups"},"scopeNote":{"en":["See also 20J05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E25","notation":["20E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local properties of groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E26","notation":["20E26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Residual properties and generalizations; residually finite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E28","notation":["20E28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Maximal subgroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E32","notation":["20E32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Simple groups"},"scopeNote":{"en":["See also 20D05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E34","notation":["20E34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General structure theorems for groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E36","notation":["20E36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphisms of infinite groups"},"scopeNote":{"en":["For automorphisms of finite groups, see 20D45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E42","notation":["20E42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groups with a BN -pair; buildings"},"scopeNote":{"en":["See also 51E24"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E45","notation":["20E45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Conjugacy classes for groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20E99","notation":["20E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Exx","notation":["20Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special aspects of infinite or finite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F05","notation":["20F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generators, relations, and presentations of groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F06","notation":["20F06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cancellation theory of groups; application of van Kampen diagrams"},"scopeNote":{"en":["See also 57M05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F10","notation":["20F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)"},"scopeNote":{"en":["See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F11","notation":["20F11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groups of finite Morley rank"},"scopeNote":{"en":["See also 03C45, 03C60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F12","notation":["20F12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutator calculus"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F14","notation":["20F14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Derived series, central series, and generalizations for groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F16","notation":["20F16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Solvable groups, supersolvable groups"},"scopeNote":{"en":["See also 20D10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F17","notation":["20F17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Formations of groups, Fitting classes"},"scopeNote":{"en":["See also 20D10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F18","notation":["20F18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nilpotent groups"},"scopeNote":{"en":["See also 20D15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F19","notation":["20F19"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of solvable and nilpotent groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F22","notation":["20F22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other classes of groups defined by subgroup chains"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F24","notation":["20F24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"FC-groups and their generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F28","notation":["20F28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphism groups of groups"},"scopeNote":{"en":["See also 20E36"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F29","notation":["20F29"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of groups as automorphism groups of algebraic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F34","notation":["20F34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fundamental groups and their automorphisms (group-theoretic aspects)"},"scopeNote":{"en":["See also 57M05, 57Sxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F36","notation":["20F36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Braid groups; Artin groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F38","notation":["20F38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other groups related to topology or analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F40","notation":["20F40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Associated Lie structures for groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F45","notation":["20F45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Engel conditions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F50","notation":["20F50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Periodic groups; locally finite groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F55","notation":["20F55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Reflection and Coxeter groups (group-theoretic aspects)"},"scopeNote":{"en":["See also 22E40, 51F15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F60","notation":["20F60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered groups (group-theoretic aspects)"},"scopeNote":{"en":["See mainly 06F15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F65","notation":["20F65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric group theory"},"scopeNote":{"en":["See also 05C25, 20E08, 57Mxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F67","notation":["20F67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperbolic groups and nonpositively curved groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F69","notation":["20F69"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic properties of groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F70","notation":["20F70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic geometry over groups; equations over groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20F99","notation":["20F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Fxx","notation":["20Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear algebraic groups and related topics"},"scopeNote":{"en":["For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G05","notation":["20G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representation theory for linear algebraic groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G07","notation":["20G07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure theory for linear algebraic groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G10","notation":["20G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cohomology theory for linear algebraic groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G15","notation":["20G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear algebraic groups over arbitrary fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G20","notation":["20G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear algebraic groups over the reals, the complexes, the quaternions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G25","notation":["20G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear algebraic groups over local fields and their integers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G30","notation":["20G30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear algebraic groups over global fields and their integers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G35","notation":["20G35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear algebraic groups over adèles and other rings and schemes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G40","notation":["20G40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear algebraic groups over finite fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G41","notation":["20G41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exceptional groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G42","notation":["20G42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum groups (quantized function algebras) and their representations"},"scopeNote":{"en":["See also 16T20, 17B37, 81R50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G43","notation":["20G43"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Schur and q-Schur algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G44","notation":["20G44"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kac-Moody groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G45","notation":["20G45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of linear algebraic groups to the sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20G99","notation":["20G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Gxx","notation":["20Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Hxx","notation":["20Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other groups of matrices"},"scopeNote":{"en":["See also 15A30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20H05","notation":["20H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unimodular groups, congruence subgroups (group-theoretic aspects)"},"scopeNote":{"en":["See also 11F06, 19B37, 22E40, 51F20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Hxx","notation":["20Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20H10","notation":["20H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuchsian groups and their generalizations (group-theoretic aspects)"},"scopeNote":{"en":["See also 11F06, 22E40, 30F35, 32Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Hxx","notation":["20Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20H15","notation":["20H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other geometric groups, including crystallographic groups"},"scopeNote":{"en":["See also 51-XX, especially 51F15, and 82D25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Hxx","notation":["20Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20H20","notation":["20H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other matrix groups over fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Hxx","notation":["20Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20H25","notation":["20H25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other matrix groups over rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Hxx","notation":["20Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20H30","notation":["20H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other matrix groups over finite fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Hxx","notation":["20Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20H99","notation":["20H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Hxx","notation":["20Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Jxx","notation":["20Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connections of group theory with homological algebra and category theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20J05","notation":["20J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological methods in group theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Jxx","notation":["20Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20J06","notation":["20J06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cohomology of groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Jxx","notation":["20Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20J15","notation":["20J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Category of groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Jxx","notation":["20Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20J99","notation":["20J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Jxx","notation":["20Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abelian groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20K01","notation":["20K01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite abelian groups"},"scopeNote":{"en":["For sumsets, see 11B13, 11P70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20K10","notation":["20K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Torsion groups, primary groups and generalized primary groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20K15","notation":["20K15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Torsion-free groups, finite rank"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20K20","notation":["20K20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Torsion-free groups, infinite rank"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20K21","notation":["20K21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mixed groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20K25","notation":["20K25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Direct sums, direct products, etc. for abelian groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20K27","notation":["20K27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subgroups of abelian groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20K30","notation":["20K30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20K35","notation":["20K35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extensions of abelian groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20K40","notation":["20K40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological and categorical methods for abelian groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20K45","notation":["20K45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological methods for abelian groups"},"scopeNote":{"en":["See also 22A05, 22B05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20K99","notation":["20K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Kxx","notation":["20Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Lxx","notation":["20Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groupoids (i.e. small categories in which all morphisms are isomorphisms)"},"scopeNote":{"en":["For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20L05","notation":["20L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groupoids (i.e. small categories in which all morphisms are isomorphisms)"},"scopeNote":{"en":["For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Lxx","notation":["20Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20L99","notation":["20L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Lxx","notation":["20Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M05","notation":["20M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free semigroups, generators and relations, word problems"},"scopeNote":{"en":["See also 03D40, 08A50, 20F10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M07","notation":["20M07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Varieties and pseudovarieties of semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M10","notation":["20M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General structure theory for semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M11","notation":["20M11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Radical theory for semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M12","notation":["20M12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ideal theory for semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M13","notation":["20M13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic theory of semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M14","notation":["20M14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutative semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M15","notation":["20M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mappings of semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M17","notation":["20M17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Regular semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M18","notation":["20M18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M19","notation":["20M19"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orthodox semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M20","notation":["20M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semigroups of transformations, relations, partitions, etc."},"scopeNote":{"en":["See also 47D03, 47H20, 54H15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M25","notation":["20M25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semigroup rings, multiplicative semigroups of rings"},"scopeNote":{"en":["See also 16S36, 16Y60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M30","notation":["20M30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representation of semigroups; actions of semigroups on sets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M32","notation":["20M32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic monoids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M35","notation":["20M35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semigroups in automata theory, linguistics, etc."},"scopeNote":{"en":["See also 03D05, 68Q70, 68T50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M50","notation":["20M50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connections of semigroups with homological algebra and category theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M75","notation":["20M75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20M99","notation":["20M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Mxx","notation":["20Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Nxx","notation":["20Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other generalizations of groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20N02","notation":["20N02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sets with a single binary operation (groupoids)"},"scopeNote":{"en":["For groupoids in connection with category theory, see 20L05; for topological groupoids, see 22A22, 58H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Nxx","notation":["20Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20N05","notation":["20N05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Loops, quasigroups"},"scopeNote":{"en":["See also 05Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Nxx","notation":["20Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20N10","notation":["20N10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ternary systems (heaps, semiheaps, heapoids, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Nxx","notation":["20Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20N15","notation":["20N15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"n-ary systems (n ≥ 3)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Nxx","notation":["20Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20N20","notation":["20N20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hypergroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Nxx","notation":["20Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20N25","notation":["20N25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy groups"},"scopeNote":{"en":["See also 03E72"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Nxx","notation":["20Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20N99","notation":["20N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Nxx","notation":["20Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20Pxx","notation":["20Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probabilistic methods in group theory"},"scopeNote":{"en":["See also 60Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20-XX","notation":["20-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20P05","notation":["20P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probabilistic methods in group theory"},"scopeNote":{"en":["See also 60Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Pxx","notation":["20Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/20P99","notation":["20P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/20Pxx","notation":["20Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological groups, Lie groups"},"scopeNote":{"en":["For transformation groups, see 54H15, 57Sxx, 58-XX; for abstract harmonic analysis, see 43-XX"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22-00","notation":["22-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to topological groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22-01","notation":["22-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to topological groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22-02","notation":["22-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to topological groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22-03","notation":["22-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of topological groups"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22-04","notation":["22-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to topological groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22-06","notation":["22-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to topological groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22-08","notation":["22-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to topological groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22-11","notation":["22-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to topological groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22Axx","notation":["22Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological and differentiable algebraic systems"},"scopeNote":{"en":["For topological rings and fields, see 12Jxx, 13Jxx, 16W80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22A05","notation":["22A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure of general topological groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Axx","notation":["22Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22A10","notation":["22A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis on general topological groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Axx","notation":["22Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22A15","notation":["22A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure of topological semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Axx","notation":["22Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22A20","notation":["22A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis on topological semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Axx","notation":["22Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22A22","notation":["22A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological groupoids (including differentiable and Lie groupoids)"},"scopeNote":{"en":["See also 58H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Axx","notation":["22Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22A25","notation":["22A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of general topological groups and semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Axx","notation":["22Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22A26","notation":["22A26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological semilattices, lattices and applications"},"scopeNote":{"en":["See also 06B30, 06B35, 06F30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Axx","notation":["22Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22A30","notation":["22A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other topological algebraic systems and their representations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Axx","notation":["22Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22A99","notation":["22A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Axx","notation":["22Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22Bxx","notation":["22Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Locally compact abelian groups (LCA groups)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22B05","notation":["22B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General properties and structure of LCA groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Bxx","notation":["22Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22B10","notation":["22B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure of group algebras of LCA groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Bxx","notation":["22Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22B99","notation":["22B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Bxx","notation":["22Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22Cxx","notation":["22Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compact groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22C05","notation":["22C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compact groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Cxx","notation":["22Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22C99","notation":["22C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Cxx","notation":["22Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Locally compact groups and their algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D05","notation":["22D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General properties and structure of locally compact groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D10","notation":["22D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unitary representations of locally compact groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D12","notation":["22D12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other representations of locally compact groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D15","notation":["22D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group algebras of locally compact groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D20","notation":["22D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of group algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D25","notation":["22D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"C ∗ -algebras and W ∗ -algebras in relation to group representations"},"scopeNote":{"en":["See also 46Lxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D30","notation":["22D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Induced representations for locally compact groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D35","notation":["22D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Duality theorems for locally compact groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D40","notation":["22D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ergodic theory on groups"},"scopeNote":{"en":["See also 28Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D45","notation":["22D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphism groups of locally compact groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D50","notation":["22D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rigidity in locally compact groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D55","notation":["22D55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kazhdan’s property (T), the Haagerup property, and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22D99","notation":["22D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Dxx","notation":["22Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lie groups"},"scopeNote":{"en":["For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E05","notation":["22E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local Lie groups"},"scopeNote":{"en":["See also 34-XX, 35-XX, 58H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E10","notation":["22E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General properties and structure of complex Lie groups"},"scopeNote":{"en":["See also 32M05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E15","notation":["22E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General properties and structure of real Lie groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E20","notation":["22E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General properties and structure of other Lie groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E25","notation":["22E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nilpotent and solvable Lie groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E27","notation":["22E27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E30","notation":["22E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis on real and complex Lie groups"},"scopeNote":{"en":["See also 33C80, 43-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E35","notation":["22E35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis on p-adic Lie groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E40","notation":["22E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discrete subgroups of Lie groups"},"scopeNote":{"en":["See also 20Hxx, 32Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E41","notation":["22E41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuous cohomologyof Lie groups"},"scopeNote":{"en":["See also 57R32, 57Txx, 58H10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E43","notation":["22E43"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure and representation of the Lorentz group"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E45","notation":["22E45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of Lie and linear algebraic groups over real fields: analytic methods"},"scopeNote":{"en":["For the purely algebraic theory, see 20G05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E46","notation":["22E46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semisimple Lie groups and their representations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E47","notation":["22E47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)"},"scopeNote":{"en":["See also 17B10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E50","notation":["22E50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of Lie and linear algebraic groups over local fields"},"scopeNote":{"en":["See also 20G05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E55","notation":["22E55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of Lie and linear algebraic groups over global fields and adèle rings"},"scopeNote":{"en":["See also 20G05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E57","notation":["22E57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric Langlands program: representation-theoretic aspects"},"scopeNote":{"en":["See also 14D24"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E60","notation":["22E60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lie algebras of Lie groups"},"scopeNote":{"en":["For the algebraic theory of Lie algebras, see 17Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E65","notation":["22E65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite-dimensional Lie groups and their Lie algebras: general properties"},"scopeNote":{"en":["See also 17B65, 58B25, 58D05 58H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E66","notation":["22E66"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis on and representations of infinite-dimensional Lie groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E67","notation":["22E67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Loop groups and related constructions, group-theoretic treatment"},"scopeNote":{"en":["See also 58D05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E70","notation":["22E70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of Lie groups to the sciences; explicit representations"},"scopeNote":{"en":["See also 81R05, 81R10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22E99","notation":["22E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Exx","notation":["22Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22Fxx","notation":["22Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncompact transformation groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22-XX","notation":["22-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22F05","notation":["22F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of group and pseudogroup actions"},"scopeNote":{"en":["For topological properties of spaces with an action, see 57S20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Fxx","notation":["22Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22F10","notation":["22F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measurable group actions"},"scopeNote":{"en":["See also 22D40, 28Dxx, 37Axx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Fxx","notation":["22Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22F30","notation":["22F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homogeneous spaces"},"scopeNote":{"en":["For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Fxx","notation":["22Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22F50","notation":["22F50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groups as automorphisms of other structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Fxx","notation":["22Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/22F99","notation":["22F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/22Fxx","notation":["22Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real functions"},"scopeNote":{"en":["See also 54C30"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26-00","notation":["26-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to real functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26-01","notation":["26-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26-02","notation":["26-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to real functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26-03","notation":["26-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of real functions"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26-04","notation":["26-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to real functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26-06","notation":["26-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to real functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26-08","notation":["26-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to real functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26-11","notation":["26-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to real functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functions of one variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A03","notation":["26A03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations: limits and generalizations, elementary topology of the line"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A06","notation":["26A06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"One-variable calculus"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A09","notation":["26A09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elementary functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A12","notation":["26A12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rate of growth of functions, orders of infinity, slowly varying functions"},"scopeNote":{"en":["See also 26A48"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A15","notation":["26A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable"},"scopeNote":{"en":["For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A16","notation":["26A16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lipschitz (Hölder) classes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A18","notation":["26A18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Iteration of real functions in one variable"},"scopeNote":{"en":["See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A21","notation":["26A21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classification of real functions; Baire classification of sets and functions"},"scopeNote":{"en":["See also 03E15, 28A05, 54C50, 54H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A24","notation":["26A24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems"},"scopeNote":{"en":["See also 28A15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A27","notation":["26A27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A30","notation":["26A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular functions, Cantor functions, functions with other special properties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A33","notation":["26A33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fractional derivatives and integrals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A36","notation":["26A36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Antidifferentiation"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A39","notation":["26A39"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Denjoy and Perron integrals, other special integrals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A42","notation":["26A42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integrals of Riemann, Stieltjes and Lebesgue type"},"scopeNote":{"en":["See also 28-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A45","notation":["26A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functions of bounded variation, generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A46","notation":["26A46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Absolutely continuous real functions in one variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A48","notation":["26A48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monotonic functions, generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A51","notation":["26A51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convexity of real functions in one variable, generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26A99","notation":["26A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Axx","notation":["26Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26Bxx","notation":["26Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functions of several variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26B05","notation":["26B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuity and differentiation questions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Bxx","notation":["26Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26B10","notation":["26B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Implicit function theorems, Jacobians, transformations with several variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Bxx","notation":["26Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26B12","notation":["26B12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Calculus of vector functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Bxx","notation":["26Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26B15","notation":["26B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integration of real functions of several variables: length, area, volume"},"scopeNote":{"en":["See also 28A75, 51M25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Bxx","notation":["26Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26B20","notation":["26B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Bxx","notation":["26Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26B25","notation":["26B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convexity of real functions of several variables, generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Bxx","notation":["26Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26B30","notation":["26B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Absolutely continuous real functions of several variables, functions of bounded variation"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Bxx","notation":["26Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26B35","notation":["26B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special properties of functions of several variables, Hölder conditions, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Bxx","notation":["26Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26B40","notation":["26B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representation and superposition of functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Bxx","notation":["26Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26B99","notation":["26B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Bxx","notation":["26Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26Cxx","notation":["26Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials, rational functions in real analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26C05","notation":["26C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real polynomials: analytic properties, etc."},"scopeNote":{"en":["See also 12Dxx, 12Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Cxx","notation":["26Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26C10","notation":["26C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real polynomials: location of zeros"},"scopeNote":{"en":["See also 12D10, 30C15, 65H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Cxx","notation":["26Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26C15","notation":["26C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real rational functions"},"scopeNote":{"en":["See also 14Pxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Cxx","notation":["26Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26C99","notation":["26C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Cxx","notation":["26Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26Dxx","notation":["26Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inequalities in real analysis"},"scopeNote":{"en":["For maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for probabilistic inequalities, see 60E15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26D05","notation":["26D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inequalities for trigonometric functions and polynomials"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Dxx","notation":["26Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26D07","notation":["26D07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inequalities involving other types of functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Dxx","notation":["26Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26D10","notation":["26D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inequalities involving derivatives and differential and integral operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Dxx","notation":["26Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26D15","notation":["26D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inequalities for sums, series and integrals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Dxx","notation":["26Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26D20","notation":["26D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other analytical inequalities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Dxx","notation":["26Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26D99","notation":["26D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Dxx","notation":["26Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Miscellaneous topics in real functions"},"scopeNote":{"en":["See also 58Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26-XX","notation":["26-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26E05","notation":["26E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real-analytic functions"},"scopeNote":{"en":["See also 32B05, 32C05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26E10","notation":["26E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"C ∞ -functions, quasi-analytic functions"},"scopeNote":{"en":["See also 58C25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26E15","notation":["26E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Calculus of functions on infinite-dimensional spaces"},"scopeNote":{"en":["See also 46G05, 58Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26E20","notation":["26E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Calculus of functions taking values in infinite-dimensional spaces"},"scopeNote":{"en":["See also 46E40, 46G10, 58Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26E25","notation":["26E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set-valued functions"},"scopeNote":{"en":["See also 28B20, 49J53, 54C60; For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26E30","notation":["26E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Non-Archimedean analysis"},"scopeNote":{"en":["See also 12J25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26E35","notation":["26E35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonstandard analysis"},"scopeNote":{"en":["See also 03H05, 28E05, 54J05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26E40","notation":["26E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Constructive real analysis"},"scopeNote":{"en":["See also 03F60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26E50","notation":["26E50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy real analysis"},"scopeNote":{"en":["See also 03E72, 28E10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26E60","notation":["26E60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Means"},"scopeNote":{"en":["See also 47A64"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26E70","notation":["26E70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real analysis on time scales or measure chains"},"scopeNote":{"en":["For dynamic equations on time scales or measure chains, see 34N05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/26E99","notation":["26E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/26Exx","notation":["26Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measure and integration"},"scopeNote":{"en":["For analysis on manifolds, see 58-XX"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28-00","notation":["28-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to measure and integration"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28-01","notation":["28-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28-02","notation":["28-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to measure and integration"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28-03","notation":["28-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of measure and integration"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28-04","notation":["28-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to measure and integration"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28-06","notation":["28-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to measure and integration"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28-08","notation":["28-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to measure and integration"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28-11","notation":["28-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to measure and integration"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical measure theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A05","notation":["28A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets"},"scopeNote":{"en":["See also 03E15, 26A21, 54H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A10","notation":["28A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real- or complex-valued set functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A12","notation":["28A12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Contents, measures, outer measures, capacities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A15","notation":["28A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract differentiation theory, differentiation of set functions"},"scopeNote":{"en":["See also 26A24"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A20","notation":["28A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A25","notation":["28A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integration with respect to measures and other set functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A33","notation":["28A33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces of measures, convergence of measures"},"scopeNote":{"en":["See also 46E27, 60Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A35","notation":["28A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measures and integrals in product spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A50","notation":["28A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integration and disintegration of measures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A51","notation":["28A51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lifting theory"},"scopeNote":{"en":["See also 46G15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A60","notation":["28A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measures on Boolean rings, measure algebras"},"scopeNote":{"en":["See also 54H10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A75","notation":["28A75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Length, area, volume, other geometric measure theory"},"scopeNote":{"en":["See also 26B15, 49Q15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A78","notation":["28A78"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hausdorff and packing measures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A80","notation":["28A80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fractals"},"scopeNote":{"en":["See also 37Fxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28A99","notation":["28A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Axx","notation":["28Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28Bxx","notation":["28Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set functions, measures and integrals with values in abstract spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28B05","notation":["28B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vector-valued set functions, measures and integrals"},"scopeNote":{"en":["See also 46G10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Bxx","notation":["28Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28B10","notation":["28B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group- or semigroup-valued set functions, measures and integrals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Bxx","notation":["28Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28B15","notation":["28B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set functions, measures and integrals with values in ordered spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Bxx","notation":["28Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28B20","notation":["28B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set-valued set functions and measures; integration of set-valued functions; measurable selections"},"scopeNote":{"en":["See also 26E25, 54C60, 54C65, 91B14"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Bxx","notation":["28Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28B99","notation":["28B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Bxx","notation":["28Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28Cxx","notation":["28Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set functions and measures on spaces with additional structure"},"scopeNote":{"en":["See also 46G12, 58C35, 58D20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28C05","notation":["28C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Cxx","notation":["28Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28C10","notation":["28C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set functions and measures on topological groups or semigroups, Haar measures, invariant measures"},"scopeNote":{"en":["See also 22Axx, 43A05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Cxx","notation":["28Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28C15","notation":["28C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set functions and measures on topological spaces (regularity of measures, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Cxx","notation":["28Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28C20","notation":["28C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)"},"scopeNote":{"en":["See also 46G12, 58C35, 58D20, 60B11"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Cxx","notation":["28Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28C99","notation":["28C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Cxx","notation":["28Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28Dxx","notation":["28Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measure-theoretic ergodic theory"},"scopeNote":{"en":["See also 11K50, 11K55, 22D40, 37Axx, 47A35, 60Fxx, 60G10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28D05","notation":["28D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measure-preserving transformations"},"scopeNote":{"en":["For measure-preserving transformations and dynamical systems, see 37A05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Dxx","notation":["28Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28D10","notation":["28D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"One-parameter continuous families of measure-preserving transformations"},"scopeNote":{"en":["For dynamical systems aspect, see 37A10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Dxx","notation":["28Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28D15","notation":["28D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General groups of measure-preserving transformations"},"scopeNote":{"en":["For dynamical systems aspects, see 37A15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Dxx","notation":["28Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28D20","notation":["28D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Entropy and other invariants"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Dxx","notation":["28Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28D99","notation":["28D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Dxx","notation":["28Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28Exx","notation":["28Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Miscellaneous topics in measure theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28-XX","notation":["28-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28E05","notation":["28E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonstandard measure theory"},"scopeNote":{"en":["See also 03H05, 26E35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Exx","notation":["28Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28E10","notation":["28E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy measure theory"},"scopeNote":{"en":["See also 03E72, 26E50, 94D05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Exx","notation":["28Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28E15","notation":["28E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other connections with logic and set theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Exx","notation":["28Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/28E99","notation":["28E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/28Exx","notation":["28Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functions of a complex variable"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/30-01","notation":["30-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30-02","notation":["30-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to functions of a complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30-03","notation":["30-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of functions of a complex variable"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30-04","notation":["30-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to functions of a complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30-06","notation":["30-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to functions of a complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30-08","notation":["30-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to functions of a complex variable"},"scopeNote":{"en":["See also 65Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30-11","notation":["30-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to functions of a complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30Axx","notation":["30Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General properties of functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30A05","notation":["30A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monogenic and polygenic functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Axx","notation":["30Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30A10","notation":["30A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inequalities in the complex plane"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Axx","notation":["30Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30A99","notation":["30A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Axx","notation":["30Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30Bxx","notation":["30Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Series expansions of functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30B10","notation":["30B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Power series (including lacunary series) in one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Bxx","notation":["30Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30B20","notation":["30B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random power series in one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Bxx","notation":["30Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30B30","notation":["30B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary behavior of power series in one complex variable; over-convergence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Bxx","notation":["30Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30B40","notation":["30B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytic continuation of functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Bxx","notation":["30Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30B50","notation":["30B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dirichlet series, exponential series and other series in one complex variable"},"scopeNote":{"en":["See also 11M41, 42-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Bxx","notation":["30Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30B60","notation":["30B60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Completeness problems, closure of a system of functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Bxx","notation":["30Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30B70","notation":["30B70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continued fractions; complex-analytic aspects"},"scopeNote":{"en":["See also 11A55, 40A15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Bxx","notation":["30Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30B99","notation":["30B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Bxx","notation":["30Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric function theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C10","notation":["30C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomials and rational functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C15","notation":["30C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)"},"scopeNote":{"en":["For algebraic theory, see 12D10; for real methods, see 26C10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C20","notation":["30C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Conformal mappings of special domains"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C25","notation":["30C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Covering theorems in conformal mapping theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C30","notation":["30C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Schwarz-Christoffel-type mappings"},"scopeNote":{"en":["See also 65E10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C35","notation":["30C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of conformal mappings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C40","notation":["30C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kernel functions in one complex variable and applications"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C45","notation":["30C45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C50","notation":["30C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Coefficient problems for univalent and multivalent functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C55","notation":["30C55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of univalent and multivalent functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C62","notation":["30C62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasiconformal mappings in the complex plane"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C65","notation":["30C65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasiconformal mappings in Rn , other generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C70","notation":["30C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extremal problems for conformal and quasiconformal mappings, variational methods"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C75","notation":["30C75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extremal problems for conformal and quasiconformal mappings, other methods"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C80","notation":["30C80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C85","notation":["30C85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Capacity and harmonic measure in the complex plane"},"scopeNote":{"en":["See also 31A15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30C99","notation":["30C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Cxx","notation":["30Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30Dxx","notation":["30Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Entire and meromorphic functions of one complex variable, and related topics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30D05","notation":["30D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable"},"scopeNote":{"en":["See also 34Mxx, 37Fxx, 39-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Dxx","notation":["30Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30D10","notation":["30D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of entire functions of one complex variable by series and integrals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Dxx","notation":["30Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30D15","notation":["30D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special classes of entire functions of one complex variable and growth estimates"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Dxx","notation":["30Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30D20","notation":["30D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Entire functions of one complex variable, general theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Dxx","notation":["30Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30D30","notation":["30D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Meromorphic functions of one complex variable, general theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Dxx","notation":["30Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30D35","notation":["30D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Value distribution of meromorphic functions of one complex variable, Nevanlinna theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Dxx","notation":["30Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30D40","notation":["30D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cluster sets, prime ends, boundary behavior"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Dxx","notation":["30Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30D45","notation":["30D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Normal functions of one complex variable, normal families"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Dxx","notation":["30Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30D60","notation":["30D60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasi-analytic and other classes of functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Dxx","notation":["30Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30D99","notation":["30D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Dxx","notation":["30Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30Exx","notation":["30Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Miscellaneous topics of analysis in the complex plane"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30E05","notation":["30E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Moment problems and interpolation problems in the complex plane"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Exx","notation":["30Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30E10","notation":["30E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Approximation in the complex plane"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Exx","notation":["30Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30E15","notation":["30E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic representations in the complex plane"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Exx","notation":["30Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30E20","notation":["30E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane"},"scopeNote":{"en":["See also 45Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Exx","notation":["30Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30E25","notation":["30E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems in the complex plane"},"scopeNote":{"en":["See also 45Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Exx","notation":["30Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30E99","notation":["30E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Exx","notation":["30Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30Fxx","notation":["30Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Riemann surfaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30F10","notation":["30F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compact Riemann surfaces and uniformization"},"scopeNote":{"en":["See also 14H15, 32G15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Fxx","notation":["30Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30F15","notation":["30F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic functions on Riemann surfaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Fxx","notation":["30Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30F20","notation":["30F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classification theory of Riemann surfaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Fxx","notation":["30Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30F25","notation":["30F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ideal boundary theory for Riemann surfaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Fxx","notation":["30Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30F30","notation":["30F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differentials on Riemann surfaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Fxx","notation":["30Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30F35","notation":["30F35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)"},"scopeNote":{"en":["See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Fxx","notation":["30Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30F40","notation":["30F40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kleinian groups (aspects of compact Riemann surfaces and uniformization)"},"scopeNote":{"en":["See also 20H10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Fxx","notation":["30Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30F45","notation":["30F45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Conformal metrics (hyperbolic, Poincaré, distance functions)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Fxx","notation":["30Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30F50","notation":["30F50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Klein surfaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Fxx","notation":["30Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30F60","notation":["30F60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Teichmüller theory"},"scopeNote":{"en":["See also 32G15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Fxx","notation":["30Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30F99","notation":["30F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Fxx","notation":["30Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30Gxx","notation":["30Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized function theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30G06","notation":["30G06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Non-Archimedean function theory ; nonstandard function theory"},"scopeNote":{"en":["See also 12J25; See also 03H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Gxx","notation":["30Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30G12","notation":["30G12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finely holomorphic functions and topological function theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Gxx","notation":["30Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30G20","notation":["30G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of Bers and Vekua type (pseudoanalytic, p-analytic, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Gxx","notation":["30Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30G25","notation":["30G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discrete analytic functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Gxx","notation":["30Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30G30","notation":["30G30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other generalizations of analytic functions (including abstract-valued functions)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Gxx","notation":["30Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30G35","notation":["30G35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functions of hypercomplex variables and generalized variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Gxx","notation":["30Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30G99","notation":["30G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Gxx","notation":["30Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces and algebras of analytic functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30H05","notation":["30H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces of bounded analytic functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30H10","notation":["30H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hardy spaces"},"scopeNote":{"en":["See also 42B30, 46E30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30H15","notation":["30H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nevanlinna spaces and Smirnov spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30H20","notation":["30H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bergman spaces and Fock spaces"},"scopeNote":{"en":["See also 46E30, 46E35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30H25","notation":["30H25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Besov spaces and Qp -spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30H30","notation":["30H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bloch spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30H35","notation":["30H35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"BMO-spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30H40","notation":["30H40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Zygmund spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30H45","notation":["30H45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"de Branges-Rovnyak spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30H50","notation":["30H50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebras of analytic functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30H80","notation":["30H80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Corona theorems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30H99","notation":["30H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Hxx","notation":["30Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30Jxx","notation":["30Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Function theory on the disc"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30J05","notation":["30J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inner functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Jxx","notation":["30Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30J10","notation":["30J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Blaschke products"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Jxx","notation":["30Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30J15","notation":["30J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular inner functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Jxx","notation":["30Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30J99","notation":["30J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Jxx","notation":["30Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30Kxx","notation":["30Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Universal holomorphic functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30K05","notation":["30K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Universal Taylor series in one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Kxx","notation":["30Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30K10","notation":["30K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Universal Dirichlet series in one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Kxx","notation":["30Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30K15","notation":["30K15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Universal functions of one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Kxx","notation":["30Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30K20","notation":["30K20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compositional universality"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Kxx","notation":["30Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30K99","notation":["30K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Kxx","notation":["30Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30Lxx","notation":["30Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis on metric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30-XX","notation":["30-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30L05","notation":["30L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric embeddings of metric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Lxx","notation":["30Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30L10","notation":["30L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasiconformal mappings in metric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Lxx","notation":["30Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30L15","notation":["30L15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inequalities in metric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Lxx","notation":["30Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/30L99","notation":["30L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/30Lxx","notation":["30Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Potential theory"},"scopeNote":{"en":["For probabilistic potential theory, see 60J45"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31-00","notation":["31-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to potential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31-01","notation":["31-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to potential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31-02","notation":["31-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to potential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31-03","notation":["31-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of potential theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31-04","notation":["31-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to potential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31-06","notation":["31-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to potential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31-08","notation":["31-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to potential theory"},"scopeNote":{"en":["See also 65Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31-11","notation":["31-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to potential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31Axx","notation":["31Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Two-dimensional potential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31A05","notation":["31A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic, subharmonic, superharmonic functions in two dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Axx","notation":["31Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31A10","notation":["31A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral representations, integral operators, integral equations methods in two dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Axx","notation":["31Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31A15","notation":["31A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions"},"scopeNote":{"en":["See also 30C85"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Axx","notation":["31Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31A20","notation":["31A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Axx","notation":["31Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31A25","notation":["31A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value and inverse problems for harmonic functions in two dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Axx","notation":["31Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31A30","notation":["31A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Axx","notation":["31Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31A35","notation":["31A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connections of harmonic functions with differential equations in two dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Axx","notation":["31Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31A99","notation":["31A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Axx","notation":["31Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31Bxx","notation":["31Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-dimensional potential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31B05","notation":["31B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic, subharmonic, superharmonic functions in higher dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Bxx","notation":["31Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31B10","notation":["31B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral representations, integral operators, integral equations methods in higher dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Bxx","notation":["31Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31B15","notation":["31B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Potentials and capacities, extremal length and related notions in higher dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Bxx","notation":["31Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31B20","notation":["31B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value and inverse problems for harmonic functions in higher dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Bxx","notation":["31Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31B25","notation":["31B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary behavior of harmonic functions in higher dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Bxx","notation":["31Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31B30","notation":["31B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biharmonic and polyharmonic equations and functions in higher dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Bxx","notation":["31Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31B35","notation":["31B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connections of harmonic functions with differential equations in higher dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Bxx","notation":["31Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31B99","notation":["31B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Bxx","notation":["31Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31Cxx","notation":["31Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of potential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31C05","notation":["31C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic, subharmonic, superharmonic functions on other spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Cxx","notation":["31Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31C10","notation":["31C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pluriharmonic and plurisubharmonic functions"},"scopeNote":{"en":["See also 32U05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Cxx","notation":["31Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31C12","notation":["31C12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Potential theory on Riemannian manifolds and other spaces"},"scopeNote":{"en":["See also 53C20; For Hodge theory, see 58A14"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Cxx","notation":["31Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31C15","notation":["31C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Potentials and capacities on other spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Cxx","notation":["31Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31C20","notation":["31C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discrete potential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Cxx","notation":["31Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31C25","notation":["31C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dirichlet forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Cxx","notation":["31Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31C35","notation":["31C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Martin boundary theory"},"scopeNote":{"en":["See also 60J50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Cxx","notation":["31Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31C40","notation":["31C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fine potential theory; fine properties of sets and functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Cxx","notation":["31Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31C45","notation":["31C45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other generalizations (nonlinear potential theory, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Cxx","notation":["31Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31C99","notation":["31C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Cxx","notation":["31Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31Dxx","notation":["31Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axiomatic potential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31D05","notation":["31D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axiomatic potential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Dxx","notation":["31Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31D99","notation":["31D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Dxx","notation":["31Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31Exx","notation":["31Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Potential theory on fractals and metric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31-XX","notation":["31-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31E05","notation":["31E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Potential theory on fractals and metric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Exx","notation":["31Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/31E99","notation":["31E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/31Exx","notation":["31Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Several complex variables and analytic spaces"},"scopeNote":{"en":["For infinitedimensional holomorphy, see also 46G20, 58B12"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32-00","notation":["32-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32-01","notation":["32-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32-02","notation":["32-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/32-04","notation":["32-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to several complex variables and analytic spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/32A36","notation":["32A36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bergman spaces of functions in several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Axx","notation":["32Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/32A40","notation":["32A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary behavior of holomorphic functions of several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Axx","notation":["32Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32A45","notation":["32A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperfunctions"},"scopeNote":{"en":["See also 46F15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Axx","notation":["32Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32A50","notation":["32A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic analysis of several complex variables"},"scopeNote":{"en":["See mainly 43-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Axx","notation":["32Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/32A60","notation":["32A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Zero sets of holomorphic functions of several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Axx","notation":["32Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32A65","notation":["32A65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Banach algebra techniques applied to functions of several complex variables"},"scopeNote":{"en":["See also 46Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Axx","notation":["32Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32A70","notation":["32A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional analysis techniques applied to functions of several complex variables"},"scopeNote":{"en":["See also 46Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Axx","notation":["32Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/32B15","notation":["32B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytic subsets of affine space"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Bxx","notation":["32Bxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/32C07","notation":["32C07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real-analytic sets, complex Nash functions"},"scopeNote":{"en":["See also 14P15, 14P20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Cxx","notation":["32Cxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/32E99","notation":["32E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Exx","notation":["32Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Fxx","notation":["32Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric convexity in several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32F10","notation":["32F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"q-convexity, q-concavity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Fxx","notation":["32Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32F17","notation":["32F17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other notions of convexity in relation to several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Fxx","notation":["32Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32F18","notation":["32F18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite-type conditions for the boundary of a domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Fxx","notation":["32Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32F27","notation":["32F27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological consequences of geometric convexity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Fxx","notation":["32Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32F32","notation":["32F32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytical consequences of geometric convexity (vanishing theorems, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Fxx","notation":["32Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32F45","notation":["32F45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Invariant metrics and pseudodistances in several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Fxx","notation":["32Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32F99","notation":["32F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Fxx","notation":["32Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Gxx","notation":["32Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deformations of analytic structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32G05","notation":["32G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deformations of complex structures"},"scopeNote":{"en":["See also 13D10, 16S80, 58H10, 58H15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Gxx","notation":["32Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32G07","notation":["32G07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deformations of special (e.g., CR) structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Gxx","notation":["32Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32G08","notation":["32G08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deformations of fiber bundles"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Gxx","notation":["32Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32G10","notation":["32G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deformations of submanifolds and subspaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Gxx","notation":["32Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32G13","notation":["32G13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex-analytic moduli problems"},"scopeNote":{"en":["For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10; See also 14H15, 14J15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Gxx","notation":["32Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32G15","notation":["32G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)"},"scopeNote":{"en":["See also 14H15, 30Fxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Gxx","notation":["32Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32G20","notation":["32G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Period matrices, variation of Hodge structure; degenerations"},"scopeNote":{"en":["See also 14D05, 14D07, 14K30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Gxx","notation":["32Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32G34","notation":["32G34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation)"},"scopeNote":{"en":["See also 34Mxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Gxx","notation":["32Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32G81","notation":["32G81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of deformations of analytic structures to the sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Gxx","notation":["32Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32G99","notation":["32G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Gxx","notation":["32Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Hxx","notation":["32Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Holomorphic mappings and correspondences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32H02","notation":["32H02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Hxx","notation":["32Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32H04","notation":["32H04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Meromorphic mappings in several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Hxx","notation":["32Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32H12","notation":["32H12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary uniqueness of mappings in several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Hxx","notation":["32Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32H25","notation":["32H25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Picard-type theorems and generalizations for several complex variables"},"scopeNote":{"en":["For function-theoretic properties, see 32A22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Hxx","notation":["32Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32H30","notation":["32H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Value distribution theory in higher dimensions"},"scopeNote":{"en":["For function-theoretic properties, see 32A22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Hxx","notation":["32Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32H35","notation":["32H35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proper holomorphic mappings, finiteness theorems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Hxx","notation":["32Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32H40","notation":["32H40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary regularity of mappings in several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Hxx","notation":["32Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32H50","notation":["32H50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Hxx","notation":["32Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32H99","notation":["32H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Hxx","notation":["32Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Jxx","notation":["32Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compact analytic spaces"},"scopeNote":{"en":["For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32J05","notation":["32J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compactification of analytic spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Jxx","notation":["32Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32J10","notation":["32J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic dependence theorems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Jxx","notation":["32Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32J15","notation":["32J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compact complex surfaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Jxx","notation":["32Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32J17","notation":["32J17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compact complex 3-folds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Jxx","notation":["32Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32J18","notation":["32J18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compact complex n-folds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Jxx","notation":["32Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32J25","notation":["32J25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transcendental methods of algebraic geometry (complex-analytic aspects)"},"scopeNote":{"en":["See also 14C30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Jxx","notation":["32Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32J27","notation":["32J27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compact Kähler manifolds: generalizations, classification"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Jxx","notation":["32Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32J81","notation":["32J81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of compact analytic spaces to the sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Jxx","notation":["32Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32J99","notation":["32J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Jxx","notation":["32Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Kxx","notation":["32Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of analytic spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32K05","notation":["32K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Banach analytic manifolds and spaces"},"scopeNote":{"en":["See also 46G20, 58Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Kxx","notation":["32Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32K07","notation":["32K07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Formal and graded complex spaces"},"scopeNote":{"en":["See also 58C50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Kxx","notation":["32Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32K12","notation":["32K12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Holomorphic maps with infinite-dimensional arguments or values"},"scopeNote":{"en":["See also 46G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Kxx","notation":["32Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32K15","notation":["32K15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differentiable functions on analytic spaces, differentiable spaces"},"scopeNote":{"en":["See also 58C25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Kxx","notation":["32Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32K99","notation":["32K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Kxx","notation":["32Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Lxx","notation":["32Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Holomorphic fiber spaces"},"scopeNote":{"en":["See also 55Rxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32L05","notation":["32L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Holomorphic bundles and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Lxx","notation":["32Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32L10","notation":["32L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sheaves and cohomology of sections of holomorphic vector bundles, general results"},"scopeNote":{"en":["See also 14F06, 14H60, 14J60, 18F20, 55N30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Lxx","notation":["32Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32L15","notation":["32L15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bundle convexity"},"scopeNote":{"en":["See also 32F10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Lxx","notation":["32Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32L20","notation":["32L20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vanishing theorems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Lxx","notation":["32Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32L25","notation":["32L25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Twistor theory, double fibrations (complex-analytic aspects)"},"scopeNote":{"en":["See also 53C28"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Lxx","notation":["32Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32L81","notation":["32L81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of holomorphic fiber spaces to the sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Lxx","notation":["32Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32L99","notation":["32L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Lxx","notation":["32Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Mxx","notation":["32Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex spaces with a group of automorphisms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32M05","notation":["32M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex Lie groups, group actions on complex spaces"},"scopeNote":{"en":["See also 22E10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Mxx","notation":["32Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32M10","notation":["32M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homogeneous complex manifolds"},"scopeNote":{"en":["See also 14M17, 57T15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Mxx","notation":["32Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32M12","notation":["32M12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Almost homogeneous manifolds and spaces"},"scopeNote":{"en":["See also 14M17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Mxx","notation":["32Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32M15","notation":["32M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)"},"scopeNote":{"en":["See also 22E10, 22E40, 53C35, 57T15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Mxx","notation":["32Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32M17","notation":["32M17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphism groups of Cn and affine manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Mxx","notation":["32Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32M18","notation":["32M18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphism groups of other complex spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Mxx","notation":["32Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32M25","notation":["32M25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex vector fields, holomorphic foliations, C-actions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Mxx","notation":["32Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32M99","notation":["32M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Mxx","notation":["32Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Nxx","notation":["32Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphic functions"},"scopeNote":{"en":["See also 11Fxx, 20H10, 22E40, 30F35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32N05","notation":["32N05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of automorphic functions of several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Nxx","notation":["32Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32N10","notation":["32N10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphic forms in several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Nxx","notation":["32Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32N15","notation":["32N15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphic functions in symmetric domains"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Nxx","notation":["32Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32N99","notation":["32N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Nxx","notation":["32Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Pxx","notation":["32Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32P05","notation":["32P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Pxx","notation":["32Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32P99","notation":["32P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Pxx","notation":["32Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q02","notation":["32Q02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special domains (Reinhardt, Hartogs, circular, tube, etc.) in Cn and complex manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q05","notation":["32Q05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Negative curvature complex manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q10","notation":["32Q10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Positive curvature complex manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q15","notation":["32Q15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kähler manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q20","notation":["32Q20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kähler-Einstein manifolds"},"scopeNote":{"en":["See also 53Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q25","notation":["32Q25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Calabi-Yau theory (complex-analytic aspects)"},"scopeNote":{"en":["See also 14J32"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q26","notation":["32Q26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Notions of stability for complex manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q28","notation":["32Q28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stein manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q30","notation":["32Q30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Uniformization of complex manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q35","notation":["32Q35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex manifolds as subdomains of Euclidean space"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q40","notation":["32Q40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Embedding theorems for complex manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q45","notation":["32Q45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperbolic and Kobayashi hyperbolic manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q55","notation":["32Q55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological aspects of complex manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q56","notation":["32Q56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Oka principle and Oka manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q57","notation":["32Q57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classification theorems for complex manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q60","notation":["32Q60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Almost complex manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q65","notation":["32Q65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pseudoholomorphic curves"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Q99","notation":["32Q99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Qxx","notation":["32Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex singularities"},"scopeNote":{"en":["See also 58Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S05","notation":["32S05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local complex singularities"},"scopeNote":{"en":["See also 14J17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S10","notation":["32S10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Invariants of analytic local rings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S15","notation":["32S15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equisingularity (topological and analytic)"},"scopeNote":{"en":["See also 14E15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S20","notation":["32S20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global theory of complex singularities; cohomological properties"},"scopeNote":{"en":["See also 14E15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S22","notation":["32S22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations with arrangements of hyperplanes"},"scopeNote":{"en":["See also 52C35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S25","notation":["32S25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex surface and hypersurface singularities"},"scopeNote":{"en":["See also 14J17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S30","notation":["32S30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deformations of complex singularities; vanishing cycles"},"scopeNote":{"en":["See also 14B07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S35","notation":["32S35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mixed Hodge theory of singular varieties (complex-analytic aspects)"},"scopeNote":{"en":["See also 14C30, 14D07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S40","notation":["32S40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monodromy; relations with differential equations and D-modules (complex-analytic aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S45","notation":["32S45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modifications; resolution of singularities (complex-analytic aspects)"},"scopeNote":{"en":["See also 14E15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S50","notation":["32S50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S55","notation":["32S55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Milnor fibration; relations with knot theory"},"scopeNote":{"en":["See also 57K10, 57K45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S60","notation":["32S60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)"},"scopeNote":{"en":["See also 58Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S65","notation":["32S65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singularities of holomorphic vector fields and foliations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S70","notation":["32S70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other operations on complex singularities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32S99","notation":["32S99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Sxx","notation":["32Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Txx","notation":["32Txx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pseudoconvex domains"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32T05","notation":["32T05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Domains of holomorphy"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Txx","notation":["32Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32T15","notation":["32T15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Strongly pseudoconvex domains"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Txx","notation":["32Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32T20","notation":["32T20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Worm domains"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Txx","notation":["32Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32T25","notation":["32T25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite-type domains"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Txx","notation":["32Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32T27","notation":["32T27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric and analytic invariants on weakly pseudoconvex boundaries"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Txx","notation":["32Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32T35","notation":["32T35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exhaustion functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Txx","notation":["32Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32T40","notation":["32T40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Peak functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Txx","notation":["32Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32T99","notation":["32T99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Txx","notation":["32Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Uxx","notation":["32Uxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pluripotential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32U05","notation":["32U05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Plurisubharmonic functions and generalizations"},"scopeNote":{"en":["See also 31C10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Uxx","notation":["32Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32U10","notation":["32U10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Plurisubharmonic exhaustion functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Uxx","notation":["32Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32U15","notation":["32U15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General pluripotential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Uxx","notation":["32Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32U20","notation":["32U20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Capacity theory and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Uxx","notation":["32Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32U25","notation":["32U25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lelong numbers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Uxx","notation":["32Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32U30","notation":["32U30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Removable sets in pluripotential theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Uxx","notation":["32Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32U35","notation":["32U35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Plurisubharmonic extremal functions, pluricomplex Green functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Uxx","notation":["32Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32U40","notation":["32U40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Currents"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Uxx","notation":["32Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32U99","notation":["32U99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Uxx","notation":["32Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32Vxx","notation":["32Vxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"CR manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32V05","notation":["32V05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"CR structures, CR operators, and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Vxx","notation":["32Vxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/32V15","notation":["32V15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"CR manifolds as boundaries of domains"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Vxx","notation":["32Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32V20","notation":["32V20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis on CR manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Vxx","notation":["32Vxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/32V30","notation":["32V30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Embeddings of CR manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Vxx","notation":["32Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32V35","notation":["32V35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite-type conditions on CR manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Vxx","notation":["32Vxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/32Wxx","notation":["32Wxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential operators in several variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32-XX","notation":["32-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32W05","notation":["32W05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"∂ and ∂-Neumann operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Wxx","notation":["32Wxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/32W30","notation":["32W30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Heat kernels in several complex variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Wxx","notation":["32Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32W50","notation":["32W50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other partial differential equations of complex analysis in several variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Wxx","notation":["32Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/32W99","notation":["32W99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/32Wxx","notation":["32Wxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/33-00","notation":["33-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33-XX","notation":["33-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33-01","notation":["33-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33-XX","notation":["33-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33-02","notation":["33-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to special functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33-XX","notation":["33-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33-03","notation":["33-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of special functions"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33-XX","notation":["33-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33-04","notation":["33-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to special functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33-XX","notation":["33-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33-06","notation":["33-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to special functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33-XX","notation":["33-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33-11","notation":["33-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to special functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33-XX","notation":["33-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33Bxx","notation":["33Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elementary classical functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33-XX","notation":["33-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33B10","notation":["33B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exponential and trigonometric functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Bxx","notation":["33Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33B15","notation":["33B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gamma, beta and polygamma functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Bxx","notation":["33Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33B20","notation":["33B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Bxx","notation":["33Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33B30","notation":["33B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher logarithm functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Bxx","notation":["33Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33B99","notation":["33B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Bxx","notation":["33Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hypergeometric functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33-XX","notation":["33-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C05","notation":["33C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical hypergeometric functions, 2 F1"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C10","notation":["33C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bessel and Airy functions, cylinder functions, 0 F1"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C15","notation":["33C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Confluent hypergeometric functions, Whittaker functions, 1 F1"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C20","notation":["33C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized hypergeometric series, p Fq"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C45","notation":["33C45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)"},"scopeNote":{"en":["For general orthogonal polynomials and functions, see also 42C05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C47","notation":["33C47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other special orthogonal polynomials and functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C50","notation":["33C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C52","notation":["33C52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orthogonal polynomials and functions associated with root systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C55","notation":["33C55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spherical harmonics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C60","notation":["33C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hypergeometric integrals and functions defined by them (E, G, H and I functions)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C65","notation":["33C65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Appell, Horn and Lauricella functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C67","notation":["33C67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hypergeometric functions associated with root systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C70","notation":["33C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other hypergeometric functions and integrals in several variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C75","notation":["33C75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic integrals as hypergeometric functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C80","notation":["33C80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connections of hypergeometric functions with groups and algebras, and related topics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C90","notation":["33C90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of hypergeometric functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33C99","notation":["33C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Cxx","notation":["33Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Basic hypergeometric functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33-XX","notation":["33-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33D05","notation":["33D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"q-gamma functions, q-beta functions and integrals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33D15","notation":["33D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Basic hypergeometric functions in one variable, r φs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33D45","notation":["33D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33D50","notation":["33D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33D52","notation":["33D52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33D60","notation":["33D60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Basic hypergeometric integrals and functions defined by them"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33D65","notation":["33D65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bibasic functions and multiple bases"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33D67","notation":["33D67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Basic hypergeometric functions associated with root systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33D70","notation":["33D70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other basic hypergeometric functions and integrals in several variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33D80","notation":["33D80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connections of basic hypergeometric functions with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and related topics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33D90","notation":["33D90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of basic hypergeometric functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33D99","notation":["33D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Dxx","notation":["33Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33Exx","notation":["33Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other special functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33-XX","notation":["33-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33E05","notation":["33E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic functions and integrals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Exx","notation":["33Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33E10","notation":["33E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lamé, Mathieu, and spheroidal wave functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Exx","notation":["33Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33E12","notation":["33E12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mittag-Leffler functions and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Exx","notation":["33Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33E15","notation":["33E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other wave functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Exx","notation":["33Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33E17","notation":["33E17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Painlevé-type functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Exx","notation":["33Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33E20","notation":["33E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other functions defined by series and integrals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Exx","notation":["33Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33E30","notation":["33E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other functions coming from differential, difference and integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Exx","notation":["33Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33E50","notation":["33E50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special functions in characteristic p (gamma functions, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Exx","notation":["33Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33E99","notation":["33E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Exx","notation":["33Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33Fxx","notation":["33Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational aspects of special functions"},"scopeNote":{"en":["For software etc., see 33-04"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33-XX","notation":["33-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33F05","notation":["33F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Numerical approximation and evaluation of special functions"},"scopeNote":{"en":["See also 65D20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Fxx","notation":["33Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33F10","notation":["33F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)"},"scopeNote":{"en":["See also 68W30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Fxx","notation":["33Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/33F99","notation":["33F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/33Fxx","notation":["33Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential equations"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34-00","notation":["34-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34-01","notation":["34-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34-02","notation":["34-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34-03","notation":["34-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of ordinary differential equations"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34-04","notation":["34-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34-06","notation":["34-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34-11","notation":["34-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A05","notation":["34A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Explicit solutions, first integrals of ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A06","notation":["34A06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A07","notation":["34A07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A08","notation":["34A08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fractional ordinary differential equations and fractional differential inclusions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A09","notation":["34A09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Implicit ordinary differential equations, differential-algebraic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A12","notation":["34A12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A25","notation":["34A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc."},"scopeNote":{"en":["See also 44-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A26","notation":["34A26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric methods in ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A30","notation":["34A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear ordinary differential equations and systems, general"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A33","notation":["34A33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary lattice differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A34","notation":["34A34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear ordinary differential equations and systems, general theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A35","notation":["34A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential equations of infinite order"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A36","notation":["34A36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discontinuous ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A37","notation":["34A37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential equations with impulses"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A38","notation":["34A38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hybrid systems of ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A40","notation":["34A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential inequalities involving functions of a single real variable"},"scopeNote":{"en":["See also 26D20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A45","notation":["34A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theoretical approximation of solutions to ordinary differential equations"},"scopeNote":{"en":["For numerical analysis, see 65Lxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A55","notation":["34A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems involving ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A60","notation":["34A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential inclusions"},"scopeNote":{"en":["See also 49J21, 49K21"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34A99","notation":["34A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Axx","notation":["34Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for ordinary differential equations"},"scopeNote":{"en":["For ordinary differential operators, see 34Lxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B05","notation":["34B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear boundary value problems for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B07","notation":["34B07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B08","notation":["34B08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Parameter dependent boundary value problems for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B09","notation":["34B09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary eigenvalue problems for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B10","notation":["34B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlocal and multipoint boundary value problems for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B15","notation":["34B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear boundary value problems for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B16","notation":["34B16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular nonlinear boundary value problems for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B18","notation":["34B18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Positive solutions to nonlinear boundary value problems for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B20","notation":["34B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Weyl theory and its generalizations for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B24","notation":["34B24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sturm-Liouville theory"},"scopeNote":{"en":["See also 34Lxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B27","notation":["34B27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Green’s functions for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B30","notation":["34B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B37","notation":["34B37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems with impulses for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B40","notation":["34B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems on infinite intervals for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B45","notation":["34B45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems on graphs and networks for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B60","notation":["34B60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of boundary value problems involving ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34B99","notation":["34B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Bxx","notation":["34Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Qualitative theory for ordinary differential equations"},"scopeNote":{"en":["See also 37-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C05","notation":["34C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological structure of integral curves, singular points, limit cycles of ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C07","notation":["34C07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C08","notation":["34C08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C10","notation":["34C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C11","notation":["34C11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Growth and boundedness of solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C12","notation":["34C12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monotone systems involving ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C14","notation":["34C14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symmetries, invariants of ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C15","notation":["34C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear oscillations and coupled oscillators for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C20","notation":["34C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transformation and reduction of ordinary differential equations and systems, normal forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C23","notation":["34C23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcation theory for ordinary differential equations"},"scopeNote":{"en":["See also 37Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C25","notation":["34C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Periodic solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C26","notation":["34C26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relaxation oscillations for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C27","notation":["34C27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Almost and pseudo-almost periodic solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C28","notation":["34C28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex behavior and chaotic systems of ordinary differential equations"},"scopeNote":{"en":["See also 37Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C29","notation":["34C29"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Averaging method for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C37","notation":["34C37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homoclinic and heteroclinic solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C40","notation":["34C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential equations and systems on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C41","notation":["34C41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equivalence and asymptotic equivalence of ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C45","notation":["34C45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Invariant manifolds for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C46","notation":["34C46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multifrequency systems of ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C55","notation":["34C55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hysteresis for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C60","notation":["34C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Qualitative investigation and simulation of ordinary differential equation models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34C99","notation":["34C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Cxx","notation":["34Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability theory for ordinary differential equations"},"scopeNote":{"en":["See also 37C75, 93Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34D05","notation":["34D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic properties of solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34D06","notation":["34D06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Synchronization of solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34D08","notation":["34D08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Characteristic and Lyapunov exponents of ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34D09","notation":["34D09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dichotomy, trichotomy of solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34D10","notation":["34D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perturbations of ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34D15","notation":["34D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular perturbations of ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34D20","notation":["34D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability of solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34D23","notation":["34D23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global stability of solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34D30","notation":["34D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structural stability and analogous concepts of solutions to ordinary differential equations"},"scopeNote":{"en":["See also 37C20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34D35","notation":["34D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability of manifolds of solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34D45","notation":["34D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Attractors of solutions to ordinary differential equations"},"scopeNote":{"en":["See also 37C70, 37D45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34D99","notation":["34D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Dxx","notation":["34Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34Exx","notation":["34Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic theory for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34E05","notation":["34E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic expansions of solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Exx","notation":["34Exx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/34E13","notation":["34E13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiple scale methods for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Exx","notation":["34Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34E15","notation":["34E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular perturbations, general theory for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Exx","notation":["34Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34E17","notation":["34E17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Canard solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Exx","notation":["34Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34E18","notation":["34E18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methods of nonstandard analysis for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Exx","notation":["34Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34E20","notation":["34E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular perturbations, turning point theory, WKB methods for ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Exx","notation":["34Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34E99","notation":["34E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Exx","notation":["34Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34Fxx","notation":["34Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential equations and systems with randomness"},"scopeNote":{"en":["See also 34K50, 60H10, 93E03"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34F05","notation":["34F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential equations and systems with randomness"},"scopeNote":{"en":["See also 34K50, 60H10, 93E03"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Fxx","notation":["34Fxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/34F15","notation":["34F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Resonance phenomena for ordinary differential equations involving randomness"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Fxx","notation":["34Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34F99","notation":["34F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Fxx","notation":["34Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34Gxx","notation":["34Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential equations in abstract spaces"},"scopeNote":{"en":["See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34G10","notation":["34G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear differential equations in abstract spaces"},"scopeNote":{"en":["See also 47D06, 47D09"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Gxx","notation":["34Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34G20","notation":["34G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear differential equations in abstract spaces"},"scopeNote":{"en":["See also 47Hxx, 47Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Gxx","notation":["34Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34G25","notation":["34G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Evolution inclusions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Gxx","notation":["34Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34G99","notation":["34G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Gxx","notation":["34Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34Hxx","notation":["34Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Control problems including ordinary differential equations"},"scopeNote":{"en":["See also 49J15, 49K15, 93C15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34H05","notation":["34H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Control problems involving ordinary differential equations"},"scopeNote":{"en":["See also 49J15, 49K15, 93C15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Hxx","notation":["34Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34H10","notation":["34H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chaos control for problems involving ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Hxx","notation":["34Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34H15","notation":["34H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stabilization of solutions to ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Hxx","notation":["34Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34H20","notation":["34H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcation control of ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Hxx","notation":["34Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34H99","notation":["34H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Hxx","notation":["34Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional-differential equations (including equations with delayed, advanced or state-dependent argument)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K04","notation":["34K04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symmetries, invariants of functional-differential equations"},"scopeNote":{"en":["See also 37C80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K05","notation":["34K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K06","notation":["34K06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K07","notation":["34K07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theoretical approximation of solutions to functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K08","notation":["34K08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral theory of functional-differential operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K09","notation":["34K09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional-differential inclusions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K10","notation":["34K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K11","notation":["34K11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Oscillation theory of functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K12","notation":["34K12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Growth, boundedness, comparison of solutions to functional-differential equations"},"scopeNote":{"en":["See also 37C35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K13","notation":["34K13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Periodic solutions to functional-differential equations"},"scopeNote":{"en":["See also 37C27"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K14","notation":["34K14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Almost and pseudo-almost periodic solutions to functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K16","notation":["34K16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Heteroclinic and homoclinic orbits of functional-differential equations"},"scopeNote":{"en":["See also 37C29"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K17","notation":["34K17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transformation and reduction of functional-differential equations and systems, normal forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K18","notation":["34K18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcation theory of functional-differential equations"},"scopeNote":{"en":["See also 37Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K19","notation":["34K19"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Invariant manifolds of functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K20","notation":["34K20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability theory of functional-differential equations"},"scopeNote":{"en":["See also 37C75"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K21","notation":["34K21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stationary solutions of functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K23","notation":["34K23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex (chaotic) behavior of solutions to functional-differential equations"},"scopeNote":{"en":["See also 37D45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K24","notation":["34K24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Synchronization of functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K25","notation":["34K25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic theory of functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K26","notation":["34K26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular perturbations of functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K27","notation":["34K27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perturbations of functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K29","notation":["34K29"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems for functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K30","notation":["34K30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional-differential equations in abstract spaces"},"scopeNote":{"en":["See also 34Gxx, 35R09, 35R10, 47Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K31","notation":["34K31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattice functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K32","notation":["34K32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Implicit functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K33","notation":["34K33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Averaging for functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K34","notation":["34K34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hybrid systems of functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K35","notation":["34K35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Control problems for functional-differential equations"},"scopeNote":{"en":["See also 49J21, 49K21, 93C23"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K36","notation":["34K36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K37","notation":["34K37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional-differential equations with fractional derivatives"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K38","notation":["34K38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional-differential inequalities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K39","notation":["34K39"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discontinuous functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K40","notation":["34K40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Neutral functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K41","notation":["34K41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional-differential equations in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K42","notation":["34K42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional-differential equations on time scales or measure chains"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K43","notation":["34K43"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional-differential equations with state-dependent arguments"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K45","notation":["34K45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional-differential equations with impulses"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K50","notation":["34K50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic functional-differential equations"},"scopeNote":{"en":["See also 34Fxx, 60Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K60","notation":["34K60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Qualitative investigation and simulation of models involving functional-differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34K99","notation":["34K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Kxx","notation":["34Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34Lxx","notation":["34Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential operators"},"scopeNote":{"en":["See also 47E05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34L05","notation":["34L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General spectral theory of ordinary differential operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Lxx","notation":["34Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34L10","notation":["34L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Lxx","notation":["34Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34L15","notation":["34L15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Lxx","notation":["34Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34L16","notation":["34L16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Lxx","notation":["34Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34L20","notation":["34L20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Lxx","notation":["34Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34L25","notation":["34L25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Scattering theory, inverse scattering involving ordinary differential operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Lxx","notation":["34Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34L30","notation":["34L30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear ordinary differential operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Lxx","notation":["34Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34L40","notation":["34L40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Lxx","notation":["34Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34L99","notation":["34L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Lxx","notation":["34Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential equations in the complex domain"},"scopeNote":{"en":["See also 30Dxx, 32G34"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M03","notation":["34M03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear ordinary differential equations and systems in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M04","notation":["34M04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear ordinary differential equations and systems in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M05","notation":["34M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Entire and meromorphic solutions to ordinary differential equations in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M10","notation":["34M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Oscillation, growth of solutions to ordinary differential equations in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M15","notation":["34M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M25","notation":["34M25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Formal solutions and transform techniques for ordinary differential equations in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M30","notation":["34M30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotics and summation methods for ordinary differential equations in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M35","notation":["34M35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M40","notation":["34M40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M45","notation":["34M45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential equations on complex manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M46","notation":["34M46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral theory for ordinary differential operators in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M50","notation":["34M50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M55","notation":["34M55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies;"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M56","notation":["34M56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Isomonodromic deformations for ordinary differential equations in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M60","notation":["34M60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent)"},"scopeNote":{"en":["See also 34E20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M65","notation":["34M65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological structure of trajectories of ordinary differential equations in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34M99","notation":["34M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Mxx","notation":["34Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34Nxx","notation":["34Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamic equations on time scales or measure chains"},"scopeNote":{"en":["For real analysis on time scales, see 26E70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34-XX","notation":["34-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34N05","notation":["34N05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamic equations on time scales or measure chains"},"scopeNote":{"en":["For real analysis on time scales or measure chains, see 26E70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Nxx","notation":["34Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/34N99","notation":["34N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/34Nxx","notation":["34Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partial differential equations"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35-00","notation":["35-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35-01","notation":["35-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35-02","notation":["35-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35-03","notation":["35-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of partial differential equations"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35-04","notation":["35-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35-06","notation":["35-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35-11","notation":["35-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General topics in partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A01","notation":["35A01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence problems for PDEs: global existence, local existence, non-existence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A02","notation":["35A02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A08","notation":["35A08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fundamental solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A09","notation":["35A09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A10","notation":["35A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cauchy-Kovalevskaya theorems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A15","notation":["35A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational methods applied to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A16","notation":["35A16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological and monotonicity methods applied to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A17","notation":["35A17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Parametrices in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A18","notation":["35A18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Wave front sets in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A20","notation":["35A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analyticity in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A21","notation":["35A21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singularity in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A22","notation":["35A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transform methods (e.g., integral transforms) applied to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A23","notation":["35A23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A24","notation":["35A24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methods of ordinary differential equations applied to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A25","notation":["35A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other special methods applied to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A27","notation":["35A27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs"},"scopeNote":{"en":["See also 32C38, 58J15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A30","notation":["35A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric theory, characteristics, transformations in context of PDEs"},"scopeNote":{"en":["See also 58J70, 58J72"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A35","notation":["35A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theoretical approximation in context of PDEs"},"scopeNote":{"en":["For numerical analysis, see 65Mxx, 65Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35A99","notation":["35A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Axx","notation":["35Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Qualitative properties of solutions to partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B05","notation":["35B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B06","notation":["35B06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symmetries, invariants, etc. in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B07","notation":["35B07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axially symmetric solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B08","notation":["35B08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Entire solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B09","notation":["35B09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Positive solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B10","notation":["35B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Periodic solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B15","notation":["35B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Almost and pseudo-almost periodic solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B20","notation":["35B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perturbations in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B25","notation":["35B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular perturbations in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B27","notation":["35B27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homogenization in context of PDEs; PDEs in media with periodic structure"},"scopeNote":{"en":["See also 74Q05, 74Q10, 76M50, 78M40, 80M40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B30","notation":["35B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs"},"scopeNote":{"en":["See also 37Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B32","notation":["35B32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcations in context of PDEs"},"scopeNote":{"en":["See also 34C23, 34F10, 34H20, 37F46, 37Gxx, 37H20, 35J20, 37L10, 37M20, 47J15, 58E05, 58E07, 58J55, 74G60, 74H60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B33","notation":["35B33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Critical exponents in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B34","notation":["35B34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Resonance in context of PDEs"},"scopeNote":{"en":["See also 34F15, 70J40, 70K28, 70K30, 81U24"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B35","notation":["35B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability in context of PDEs"},"scopeNote":{"en":["See also 34Dxx, 37B25, 37C20, 37C75, 37F15, 37J25, 37K45, 37L15, 49K40, 58K25, 93Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B36","notation":["35B36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pattern formations in context of PDEs"},"scopeNote":{"en":["See also 92C15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B38","notation":["35B38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Critical points of functionals in context of PDEs (e.g., energy functionals)"},"scopeNote":{"en":["See also 57R70, 58K05, 58E05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B40","notation":["35B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic behavior of solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B41","notation":["35B41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Attractors"},"scopeNote":{"en":["See also 34D45, 37B35, 37C70, 37D45, 37G35, 37L30, 37M22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B42","notation":["35B42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inertial manifolds"},"scopeNote":{"en":["See also 37L25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B44","notation":["35B44"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Blow-up in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B45","notation":["35B45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"A priori estimates in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B50","notation":["35B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Maximum principles in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B51","notation":["35B51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Comparison principles in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B53","notation":["35B53"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B60","notation":["35B60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuation and prolongation of solutions to PDEs"},"scopeNote":{"en":["See also 58A15, 58A17, 58Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B65","notation":["35B65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Smoothness and regularity of solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35B99","notation":["35B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Bxx","notation":["35Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Cxx","notation":["35Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of solutions to partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35C05","notation":["35C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Solutions to PDEs in closed form"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Cxx","notation":["35Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35C06","notation":["35C06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Self-similar solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Cxx","notation":["35Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35C07","notation":["35C07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Traveling wave solutions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Cxx","notation":["35Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35C08","notation":["35C08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Soliton solutions"},"scopeNote":{"en":["See also 37K40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Cxx","notation":["35Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35C09","notation":["35C09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Trigonometric solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Cxx","notation":["35Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35C10","notation":["35C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Series solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Cxx","notation":["35Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35C11","notation":["35C11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomial solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Cxx","notation":["35Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35C15","notation":["35C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral representations of solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Cxx","notation":["35Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35C20","notation":["35C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic expansions of solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Cxx","notation":["35Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35C99","notation":["35C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Cxx","notation":["35Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Dxx","notation":["35Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized solutions to partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35D30","notation":["35D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Weak solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Dxx","notation":["35Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35D35","notation":["35D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Strong solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Dxx","notation":["35Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35D40","notation":["35D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Viscosity solutions to PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Dxx","notation":["35Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35D99","notation":["35D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Dxx","notation":["35Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Exx","notation":["35Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partial differential equations and systems of partial differential equations with constant coefficients"},"scopeNote":{"en":["See also 35N05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35E05","notation":["35E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fundamental solutions to PDEs and systems of PDEs with constant coefficients"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Exx","notation":["35Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35E10","notation":["35E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convexity properties of solutions to PDEs and systems of PDEs with constant coefficients"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Exx","notation":["35Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35E15","notation":["35E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for PDEs and systems of PDEs with constant coefficients"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Exx","notation":["35Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35E20","notation":["35E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of PDEs and systems of PDEs with constant coefficients"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Exx","notation":["35Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35E99","notation":["35E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Exx","notation":["35Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Fxx","notation":["35Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General first-order partial differential equations and systems of first-order partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35F05","notation":["35F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear first-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Fxx","notation":["35Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35F10","notation":["35F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for linear first-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Fxx","notation":["35Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35F15","notation":["35F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for linear first-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Fxx","notation":["35Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35F16","notation":["35F16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for linear first-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Fxx","notation":["35Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35F20","notation":["35F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear first-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Fxx","notation":["35Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35F21","notation":["35F21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hamilton-Jacobi equations"},"scopeNote":{"en":["For calculus of variations and optimal control, see 49Lxx; for mechanics of particles and systems, see 70H20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Fxx","notation":["35Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35F25","notation":["35F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for nonlinear first-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Fxx","notation":["35Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35F30","notation":["35F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for nonlinear first-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Fxx","notation":["35Fxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/35F45","notation":["35F45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for systems of linear first-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Fxx","notation":["35Fxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/35G05","notation":["35G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G10","notation":["35G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for linear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G15","notation":["35G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for linear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G16","notation":["35G16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for linear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G20","notation":["35G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G25","notation":["35G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for nonlinear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G30","notation":["35G30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for nonlinear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G31","notation":["35G31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for nonlinear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G35","notation":["35G35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Systems of linear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G40","notation":["35G40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for systems of linear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G45","notation":["35G45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for systems of linear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G46","notation":["35G46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for systems of linear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G50","notation":["35G50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Systems of nonlinear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G55","notation":["35G55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for systems of nonlinear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G60","notation":["35G60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for systems of nonlinear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G61","notation":["35G61"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for systems of nonlinear higher-order PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35G99","notation":["35G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Gxx","notation":["35Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Hxx","notation":["35Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Close-to-elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35H10","notation":["35H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hypoelliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Hxx","notation":["35Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35H20","notation":["35H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subelliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Hxx","notation":["35Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35H30","notation":["35H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasielliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Hxx","notation":["35Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35H99","notation":["35H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Hxx","notation":["35Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic equations and elliptic systems"},"scopeNote":{"en":["For global analysis, analysis on manifolds, see 58J10, 58J20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J05","notation":["35J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation"},"scopeNote":{"en":["See also 31Axx, 31Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J08","notation":["35J08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Green’s functions for elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J10","notation":["35J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Schrödinger operator, Schrödinger equation"},"scopeNote":{"en":["For ordinary differential equations, see 34L40; for operator theory, see 47D08; for quantum theory, see 81Q05; for statistical mechanics, see 82B44"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J15","notation":["35J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Second-order elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J20","notation":["35J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational methods for second-order elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J25","notation":["35J25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for second-order elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J30","notation":["35J30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-order elliptic equations"},"scopeNote":{"en":["See also 31A30, 31B30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J35","notation":["35J35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational methods for higher-order elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J40","notation":["35J40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for higher-order elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J46","notation":["35J46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"First-order elliptic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J47","notation":["35J47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Second-order elliptic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J48","notation":["35J48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-order elliptic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J50","notation":["35J50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational methods for elliptic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J56","notation":["35J56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for first-order elliptic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J57","notation":["35J57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for second-order elliptic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J58","notation":["35J58"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for higher-order elliptic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J60","notation":["35J60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J61","notation":["35J61"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semilinear elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J62","notation":["35J62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasilinear elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J65","notation":["35J65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear boundary value problems for linear elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J66","notation":["35J66"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear boundary value problems for nonlinear elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J67","notation":["35J67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary values of solutions to elliptic equations and elliptic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J70","notation":["35J70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Degenerate elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J75","notation":["35J75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular elliptic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J86","notation":["35J86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators"},"scopeNote":{"en":["See also 35R35, 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J87","notation":["35J87"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators"},"scopeNote":{"en":["See also 35R35, 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J88","notation":["35J88"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unilateral problems for elliptic systems and systems of variational inequalities with elliptic operators"},"scopeNote":{"en":["See also 35R35, 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J91","notation":["35J91"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J92","notation":["35J92"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasilinear elliptic equations with p-Laplacian"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J93","notation":["35J93"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasilinear elliptic equations with mean curvature operator"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J94","notation":["35J94"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic equations with infinity-Laplacian"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J96","notation":["35J96"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monge-Ampère equations"},"scopeNote":{"en":["For complex Monge-Ampère operators, see 32W20; for parabolic Monge-Ampère equations, see 35K96"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35J99","notation":["35J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Jxx","notation":["35Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Parabolic equations and parabolic systems"},"scopeNote":{"en":["For global analysis, analysis on manifolds, see 58J35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K05","notation":["35K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Heat equation"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K08","notation":["35K08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Heat kernel"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K10","notation":["35K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Second-order parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K15","notation":["35K15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for second-order parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K20","notation":["35K20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for second-order parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K25","notation":["35K25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-order parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K30","notation":["35K30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for higher-order parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K35","notation":["35K35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for higher-order parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K40","notation":["35K40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Second-order parabolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K41","notation":["35K41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-order parabolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K45","notation":["35K45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for second-order parabolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K46","notation":["35K46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for higher-order parabolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K51","notation":["35K51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for second-order parabolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K52","notation":["35K52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for higher-order parabolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K55","notation":["35K55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K57","notation":["35K57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Reaction-diffusion equations"},"scopeNote":{"en":["For diffusion processes and reaction effects, see 47D07, 58J65, 60J60, 60J70, 74N25, 76R50, 76V05, 80A23, 82B24, 82C24, 92E20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K58","notation":["35K58"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semilinear parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K59","notation":["35K59"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasilinear parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K60","notation":["35K60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K61","notation":["35K61"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K65","notation":["35K65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Degenerate parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K67","notation":["35K67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K70","notation":["35K70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ultraparabolic equations, pseudoparabolic equations, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K85","notation":["35K85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators"},"scopeNote":{"en":["See also 35R35, 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K86","notation":["35K86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators"},"scopeNote":{"en":["See also 35R35, 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K87","notation":["35K87"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators"},"scopeNote":{"en":["See also 35R35, 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K90","notation":["35K90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract parabolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K91","notation":["35K91"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K92","notation":["35K92"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasilinear parabolic equations with p-Laplacian"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K93","notation":["35K93"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasilinear parabolic equations with mean curvature operator"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K96","notation":["35K96"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Parabolic Monge-Ampère equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35K99","notation":["35K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Kxx","notation":["35Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperbolic equations and hyperbolic systems"},"scopeNote":{"en":["For global analysis, see 58J45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L02","notation":["35L02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"First-order hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L03","notation":["35L03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for first-order hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L04","notation":["35L04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for first-order hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L05","notation":["35L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Wave equation"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L10","notation":["35L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Second-order hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L15","notation":["35L15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for second-order hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L20","notation":["35L20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for second-order hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L25","notation":["35L25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-order hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L30","notation":["35L30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for higher-order hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L35","notation":["35L35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for higher-order hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L40","notation":["35L40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"First-order hyperbolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L45","notation":["35L45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for first-order hyperbolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L50","notation":["35L50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for first-order hyperbolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L51","notation":["35L51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Second-order hyperbolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L52","notation":["35L52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for second-order hyperbolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L53","notation":["35L53"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for second-order hyperbolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L55","notation":["35L55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-order hyperbolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L56","notation":["35L56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for higher-order hyperbolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L57","notation":["35L57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for higher-order hyperbolic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L60","notation":["35L60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"First-order nonlinear hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L65","notation":["35L65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperbolic conservation laws"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L67","notation":["35L67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Shocks and singularities for hyperbolic equations"},"scopeNote":{"en":["See also 58Kxx, 74J40, 76L05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L70","notation":["35L70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Second-order nonlinear hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L71","notation":["35L71"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Second-order semilinear hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L72","notation":["35L72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Second-order quasilinear hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L75","notation":["35L75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-order nonlinear hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L76","notation":["35L76"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-order semilinear hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L77","notation":["35L77"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-order quasilinear hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L80","notation":["35L80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Degenerate hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L81","notation":["35L81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L82","notation":["35L82"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pseudohyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L85","notation":["35L85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators"},"scopeNote":{"en":["See also 35R35, 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L86","notation":["35L86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unilateral problems for nonlinear hyperbolic equations and variational inequalities with nonlinear hyperbolic operators"},"scopeNote":{"en":["See also 35R35, 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L87","notation":["35L87"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unilateral problems for hyperbolic systems and systems of variational inequalities with hyperbolic operators"},"scopeNote":{"en":["See also 35R35, 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L90","notation":["35L90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract hyperbolic equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35L99","notation":["35L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Lxx","notation":["35Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partial differential equations of mixed type and mixed-type systems of partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35M10","notation":["35M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs of mixed type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35M11","notation":["35M11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for PDEs of mixed type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35M12","notation":["35M12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for PDEs of mixed type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35M13","notation":["35M13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for PDEs of mixed type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35M30","notation":["35M30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mixed-type systems of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35M31","notation":["35M31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for mixed-type systems of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35M32","notation":["35M32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for mixed-type systems of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35M33","notation":["35M33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for mixed-type systems of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35M85","notation":["35M85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unilateral problems for linear PDEs of mixed type and variational inequalities with partial differential operators of mixed type"},"scopeNote":{"en":["See also 35R35, 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35M86","notation":["35M86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unilateral problems for nonlinear PDEs of mixed type and variational inequalities with nonlinear partial differential operators of mixed type"},"scopeNote":{"en":["See also 35R35, 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35M87","notation":["35M87"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unilateral problems for mixed-type systems of PDEs and systems of variational inequalities with partial differential operators of mixed type"},"scopeNote":{"en":["See also 35R35, 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35M99","notation":["35M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Mxx","notation":["35Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Nxx","notation":["35Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Overdetermined problems for partial differential equations and systems of partial differential equations"},"scopeNote":{"en":["For global analysis, see 58Hxx, 58J10, 58J15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35N05","notation":["35N05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Overdetermined systems of PDEs with constant coefficients"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Nxx","notation":["35Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35N10","notation":["35N10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Overdetermined systems of PDEs with variable coefficients"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Nxx","notation":["35Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35N15","notation":["35N15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"∂-Neumann problems and formal complexes in context of PDEs"},"scopeNote":{"en":["See also 32W05, 32W10, 58J10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Nxx","notation":["35Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35N20","notation":["35N20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Overdetermined initial value problems for PDEs and systems of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Nxx","notation":["35Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35N25","notation":["35N25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Overdetermined boundary value problems for PDEs and systems of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Nxx","notation":["35Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35N30","notation":["35N30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Overdetermined initial-boundary value problems for PDEs and systems of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Nxx","notation":["35Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35N99","notation":["35N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Nxx","notation":["35Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Pxx","notation":["35Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral theory and eigenvalue problems for partial differential equations"},"scopeNote":{"en":["For operator theory, see 47Axx, 47Bxx, 47F05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35P05","notation":["35P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General topics in linear spectral theory for PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Pxx","notation":["35Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35P10","notation":["35P10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Completeness of eigenfunctions and eigenfunction expansions in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Pxx","notation":["35Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35P15","notation":["35P15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Estimates of eigenvalues in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Pxx","notation":["35Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35P20","notation":["35P20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic distributions of eigenvalues in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Pxx","notation":["35Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35P25","notation":["35P25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Scattering theory for PDEs"},"scopeNote":{"en":["See also 47A40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Pxx","notation":["35Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35P30","notation":["35P30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Pxx","notation":["35Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35P99","notation":["35P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Pxx","notation":["35Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partial differential equations of mathematical physics and other areas of application"},"scopeNote":{"en":["See also 35J05, 35J10, 35K05, 35L05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q05","notation":["35Q05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Euler-Poisson-Darboux equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q07","notation":["35Q07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuchsian PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q15","notation":["35Q15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Riemann-Hilbert problems in context of PDEs"},"scopeNote":{"en":["See also 30E25, 31A25, 31B20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q20","notation":["35Q20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boltzmann equations"},"scopeNote":{"en":["For fluid mechanics, see 76P05; for statistical mechanics, see 82B40, 82C40, 82D05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q30","notation":["35Q30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Navier-Stokes equations"},"scopeNote":{"en":["For fluid mechanics, see 76D05, 76D07, 76N10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q31","notation":["35Q31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Euler equations"},"scopeNote":{"en":["For fluid mechanics, see 76D05, 76D07, 76N10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q35","notation":["35Q35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q40","notation":["35Q40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with quantum mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q41","notation":["35Q41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Time-dependent Schrödinger equations and Dirac equations"},"scopeNote":{"en":["For quantum theory, see 81Q05; for relativity and gravitational theory, see 83A05, 83C10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q51","notation":["35Q51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Soliton equations"},"scopeNote":{"en":["For dynamical systems and ergodic theory, see 37K40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q53","notation":["35Q53"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"KdV equations (Korteweg-de Vries equations)"},"scopeNote":{"en":["For dynamical systems and ergodic theory, see 37K10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q55","notation":["35Q55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"NLS equations (nonlinear Schrödinger equations)"},"scopeNote":{"en":["For dynamical systems and ergodic theory, see 37K10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q56","notation":["35Q56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ginzburg-Landau equations"},"scopeNote":{"en":["For optics and electromagnetic theory, see 78A25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q60","notation":["35Q60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q61","notation":["35Q61"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Maxwell equations"},"scopeNote":{"en":["For optics and electromagnetic theory, see 78A25; for relativity and gravitational theory, see 83C22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q62","notation":["35Q62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with statistics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q68","notation":["35Q68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q70","notation":["35Q70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with mechanics of particles and systems of particles"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q74","notation":["35Q74"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with mechanics of deformable solids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q75","notation":["35Q75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q76","notation":["35Q76"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Einstein equations"},"scopeNote":{"en":["For several complex variables and analytic spaces, see 32Q40; for differential geometry, see 53C07; for relativity and gravitational theory, see 83C05, 83C25, 83D05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q79","notation":["35Q79"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with classical thermodynamics and heat transfer"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q80","notation":["35Q80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transport equations"},"scopeNote":{"en":["For calculus of variations and optimal control, see 49Q20; for fluid mechanics, see 76F25; for statistical mechanics, see 82C70, 82D75; for operations research, see 90B06; for mathematical programming, see 90C08"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q81","notation":["35Q81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with semiconductor devices"},"scopeNote":{"en":["For statistical mechanics, see 82D37"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q82","notation":["35Q82"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q83","notation":["35Q83"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vlasov equations"},"scopeNote":{"en":["For statistical mechanics, see 82C70, 82D75"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q84","notation":["35Q84"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fokker-Planck equations"},"scopeNote":{"en":["For fluid mechanics, see 76X05, 76W05; for statistical mechanics, see 82C31"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q85","notation":["35Q85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with astronomy and astrophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q86","notation":["35Q86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with geophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q89","notation":["35Q89"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with mean field game theory"},"scopeNote":{"en":["For calculus of variations and optimal control, see 49N80; for game theory, see 91A16"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q90","notation":["35Q90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with mathematical programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q91","notation":["35Q91"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with game theory, economics, social and behavioral sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q92","notation":["35Q92"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with biology, chemistry and other natural sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q93","notation":["35Q93"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with control and optimization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q94","notation":["35Q94"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs in connection with information and communication"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Q99","notation":["35Q99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Qxx","notation":["35Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Miscellaneous topics in partial differential equations"},"scopeNote":{"en":["For equations on manifolds, see 32Wxx, 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDEs, see 60H15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R01","notation":["35R01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs on manifolds"},"scopeNote":{"en":["See also 32Wxx, 53Cxx, 58Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R02","notation":["35R02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs on graphs and networks (ramified or polygonal spaces)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R03","notation":["35R03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs on Heisenberg groups, Lie groups, Carnot groups, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R05","notation":["35R05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs with low regular coefficients and/or low regular data"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R06","notation":["35R06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs with measure"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R07","notation":["35R07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs on time scales"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R09","notation":["35R09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral partial differential equations"},"scopeNote":{"en":["See also 45Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R10","notation":["35R10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R11","notation":["35R11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fractional partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R12","notation":["35R12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Impulsive partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R13","notation":["35R13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R15","notation":["35R15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables)"},"scopeNote":{"en":["See also 46Gxx, 58D25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R20","notation":["35R20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)"},"scopeNote":{"en":["See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R25","notation":["35R25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ill-posed problems for PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R30","notation":["35R30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems for PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R35","notation":["35R35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free boundary problems for PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R37","notation":["35R37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Moving boundary problems for PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R45","notation":["35R45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partial differential inequalities and systems of partial differential inequalities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R50","notation":["35R50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs of infinite order"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R60","notation":["35R60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs with randomness, stochastic partial differential equations"},"scopeNote":{"en":["See also 60H15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R70","notation":["35R70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"PDEs with multivalued right-hand sides"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35R99","notation":["35R99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Rxx","notation":["35Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35Sxx","notation":["35Sxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pseudodifferential operators and other generalizations of partial differential operators"},"scopeNote":{"en":["For operator theory, see 47G30, 58J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35-XX","notation":["35-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35S05","notation":["35S05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pseudodifferential operators as generalizations of partial differential operators"},"scopeNote":{"en":["See also 32W25, 47G30, 47L80, 58J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Sxx","notation":["35Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35S10","notation":["35S10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial value problems for PDEs with pseudodifferential operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Sxx","notation":["35Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35S15","notation":["35S15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for PDEs with pseudodifferential operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Sxx","notation":["35Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35S16","notation":["35S16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Initial-boundary value problems for PDEs with pseudodifferential operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Sxx","notation":["35Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35S30","notation":["35S30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fourier integral operators applied to PDEs"},"scopeNote":{"en":["See also 43A32, 58J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Sxx","notation":["35Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35S35","notation":["35S35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc."},"scopeNote":{"en":["See also 32C38, 32S40, 32S60, 58J15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Sxx","notation":["35Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35S50","notation":["35S50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Paradifferential operators as generalizations of partial differential operators in context of PDEs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Sxx","notation":["35Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/35S99","notation":["35S99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/35Sxx","notation":["35Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems and ergodic theory"},"scopeNote":{"en":["See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37-00","notation":["37-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to dynamical systems and ergodic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37-01","notation":["37-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37-02","notation":["37-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37-03","notation":["37-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of dynamical systems and ergodic theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37-04","notation":["37-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37-06","notation":["37-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37-11","notation":["37-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to dynamical systems and ergodic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ergodic theory"},"scopeNote":{"en":["See also 28Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A05","notation":["37A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical aspects of measure-preserving transformations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A10","notation":["37A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems involving one-parameter continuous families of measure-preserving transformations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A15","notation":["37A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General groups of measure-preserving transformations and dynamical systems"},"scopeNote":{"en":["See mainly 22Fxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A17","notation":["37A17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homogeneous flows"},"scopeNote":{"en":["See also 22Fxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A20","notation":["37A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A25","notation":["37A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ergodicity, mixing, rates of mixing"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A30","notation":["37A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ergodic theorems, spectral theory, Markov operators"},"scopeNote":{"en":["For operator ergodic theory, see mainly 47A35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A35","notation":["37A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Entropy and other invariants, isomorphism, classification in ergodic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A40","notation":["37A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonsingular (and infinite-measure preserving) transformations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A45","notation":["37A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations between ergodic theory and number theory"},"scopeNote":{"en":["See also 11Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A46","notation":["37A46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations between ergodic theory and harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A50","notation":["37A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems and their relations with probability theory and stochastic processes"},"scopeNote":{"en":["See also 60Fxx, 60G10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A55","notation":["37A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems and the theory of C ∗ -algebras"},"scopeNote":{"en":["See mainly 46L55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A60","notation":["37A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical aspects of statistical mechanics"},"scopeNote":{"en":["See also 82Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37A99","notation":["37A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Axx","notation":["37Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B02","notation":["37B02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamics in general topological spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B05","notation":["37B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B10","notation":["37B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symbolic dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B15","notation":["37B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical aspects of cellular automata"},"scopeNote":{"en":["For computational aspects, see 68Q80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B20","notation":["37B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Notions of recurrence and recurrent behavior in dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B25","notation":["37B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability of topological dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B30","notation":["37B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Index theory for dynamical systems, Morse-Conley indices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B35","notation":["37B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B40","notation":["37B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological entropy"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B45","notation":["37B45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continua theory in dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B50","notation":["37B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multidimensional shifts of finite type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B52","notation":["37B52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Tiling dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B55","notation":["37B55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological dynamics of nonautonomous systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B65","notation":["37B65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37B99","notation":["37B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Bxx","notation":["37Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Smooth dynamical systems: general theory"},"scopeNote":{"en":["See also 34Cxx, 34Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C05","notation":["37C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems involving smooth mappings and diffeomorphisms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C10","notation":["37C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamics induced by flows and semiflows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C15","notation":["37C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C20","notation":["37C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generic properties, structural stability of dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C25","notation":["37C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fixed points and periodic points of dynamical systems; fixed-point index theory, local dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C27","notation":["37C27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Periodic orbits of vector fields and flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C29","notation":["37C29"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homoclinic and heteroclinic orbits for dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C30","notation":["37C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C35","notation":["37C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orbit growth in dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C40","notation":["37C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Smooth ergodic theory, invariant measures for smooth dynamical systems"},"scopeNote":{"en":["See also 37Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C45","notation":["37C45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dimension theory of smooth dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C50","notation":["37C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C55","notation":["37C55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Periodic and quasi-periodic flows and diffeomorphisms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C60","notation":["37C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonautonomous smooth dynamical systems"},"scopeNote":{"en":["See also 37B55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C65","notation":["37C65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monotone flows as dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C70","notation":["37C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Attractors and repellers of smooth dynamical systems and their topological structure"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C75","notation":["37C75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability theory for smooth dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C80","notation":["37C80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symmetries and invariants of dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C81","notation":["37C81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equivariant dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C83","notation":["37C83"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems with singularities (billiards, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C85","notation":["37C85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamics induced by group actions other than Z and R, and C"},"scopeNote":{"en":["See mainly 22Fxx, and also 32M25, 57R30, 57Sxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C86","notation":["37C86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foliations generated by dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37C99","notation":["37C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Cxx","notation":["37Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Dxx","notation":["37Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems with hyperbolic behavior"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37D05","notation":["37D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems with hyperbolic orbits and sets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Dxx","notation":["37Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37D10","notation":["37D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Invariant manifold theory for dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Dxx","notation":["37Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37D15","notation":["37D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Morse-Smale systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Dxx","notation":["37Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37D20","notation":["37D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Dxx","notation":["37Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37D25","notation":["37D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Dxx","notation":["37Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37D30","notation":["37D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partially hyperbolic systems and dominated splittings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Dxx","notation":["37Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37D35","notation":["37D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Thermodynamic formalism, variational principles, equilibrium states for dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Dxx","notation":["37Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37D40","notation":["37D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Dxx","notation":["37Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37D45","notation":["37D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Strange attractors, chaotic dynamics of systems with hyperbolic behavior"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Dxx","notation":["37Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37D99","notation":["37D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Dxx","notation":["37Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Exx","notation":["37Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Low-dimensional dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37E05","notation":["37E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems involving maps of the interval (piecewise continuous, continuous, smooth)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Exx","notation":["37Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37E10","notation":["37E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems involving maps of the circle"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Exx","notation":["37Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37E15","notation":["37E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial dynamics (types of periodic orbits)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Exx","notation":["37Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37E20","notation":["37E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Universality and renormalization of dynamical systems"},"scopeNote":{"en":["See also 37F25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Exx","notation":["37Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37E25","notation":["37E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems involving maps of trees and graphs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Exx","notation":["37Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37E30","notation":["37E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Exx","notation":["37Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37E35","notation":["37E35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Flows on surfaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Exx","notation":["37Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37E40","notation":["37E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical aspects of twist maps"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Exx","notation":["37Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37E45","notation":["37E45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rotation numbers and vectors"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Exx","notation":["37Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37E99","notation":["37E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Exx","notation":["37Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems over complex numbers"},"scopeNote":{"en":["See also 30D05, 32H50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F05","notation":["37F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems involving relations and correspondences in one complex variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F10","notation":["37F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets"},"scopeNote":{"en":["See also 32A10, 32A20, 32H02, 32H04"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F12","notation":["37F12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Critical orbits for holomorphic dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F15","notation":["37F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F20","notation":["37F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorics and topology in relation with holomorphic dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F25","notation":["37F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Renormalization of holomorphic dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F30","notation":["37F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F32","notation":["37F32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuchsian and Kleinian groups as dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F34","notation":["37F34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Teichmüller theory; moduli spaces of holomorphic dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F35","notation":["37F35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Conformal densities and Hausdorff dimension for holomorphic dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F40","notation":["37F40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric limits in holomorphic dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F45","notation":["37F45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F46","notation":["37F46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F50","notation":["37F50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Small divisors, rotation domains and linearization in holomorphic dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F75","notation":["37F75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical aspects of holomorphic foliations and vector fields"},"scopeNote":{"en":["See also 32M25, 32S65, 34Mxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F80","notation":["37F80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-dimensional holomorphic and meromorphic dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37F99","notation":["37F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Fxx","notation":["37Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Gxx","notation":["37Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local and nonlocal bifurcation theory for dynamical systems"},"scopeNote":{"en":["See also 34C23, 34K18"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37G05","notation":["37G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Normal forms for dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Gxx","notation":["37Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37G10","notation":["37G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcations of singular points in dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Gxx","notation":["37Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37G15","notation":["37G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcations of limit cycles and periodic orbits in dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Gxx","notation":["37Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37G20","notation":["37G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperbolic singular points with homoclinic trajectories in dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Gxx","notation":["37Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37G25","notation":["37G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcations connected with nontransversal intersection in dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Gxx","notation":["37Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37G30","notation":["37G30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite nonwandering sets arising in bifurcations of dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Gxx","notation":["37Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37G35","notation":["37G35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical aspects of attractors and their bifurcations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Gxx","notation":["37Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37G40","notation":["37G40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical aspects of symmetries, equivariant bifurcation theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Gxx","notation":["37Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37G99","notation":["37G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Gxx","notation":["37Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Hxx","notation":["37Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random dynamical systems"},"scopeNote":{"en":["See also 15B52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37H05","notation":["37H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of random and stochastic dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Hxx","notation":["37Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37H10","notation":["37H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generation, random and stochastic difference and differential equations"},"scopeNote":{"en":["See also 34F05, 34K50, 60H10, 60H15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Hxx","notation":["37Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37H12","notation":["37H12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random iteration"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Hxx","notation":["37Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37H15","notation":["37H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents"},"scopeNote":{"en":["See also 34D08, 37Axx, 37Cxx, 37Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Hxx","notation":["37Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37H20","notation":["37H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcation theory for random and stochastic dynamical systems"},"scopeNote":{"en":["See also 37Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Hxx","notation":["37Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37H30","notation":["37H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability theory for random and stochastic dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Hxx","notation":["37Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37H99","notation":["37H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Hxx","notation":["37Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems"},"scopeNote":{"en":["See also 53Dxx, 70Fxx, 70Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J05","notation":["37J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J10","notation":["37J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symplectic and canonical mappings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J12","notation":["37J12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fixed points and periodic points of finite-dimensional Hamiltonian and Lagrangian systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J20","notation":["37J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J25","notation":["37J25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability problems for finite-dimensional Hamiltonian and Lagrangian systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J30","notation":["37J30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J35","notation":["37J35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J37","notation":["37J37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J38","notation":["37J38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J39","notation":["37J39"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.)"},"scopeNote":{"en":["See also 53D20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J40","notation":["37J40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J45","notation":["37J45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J50","notation":["37J50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J55","notation":["37J55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Contact systems"},"scopeNote":{"en":["See also 53D10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J60","notation":["37J60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonholonomic dynamical systems"},"scopeNote":{"en":["See also 70F25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J65","notation":["37J65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J70","notation":["37J70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Completely integrable discrete dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37J99","notation":["37J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Jxx","notation":["37Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems"},"scopeNote":{"en":["See also 35Axx, 35Qxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K05","notation":["37K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K10","notation":["37K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K15","notation":["37K15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K20","notation":["37K20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions"},"scopeNote":{"en":["See also 14H70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K25","notation":["37K25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K30","notation":["37K30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K35","notation":["37K35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K40","notation":["37K40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K45","notation":["37K45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K50","notation":["37K50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K55","notation":["37K55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perturbations, KAM for infinite-dimensional Hamiltonian and Lagrangian systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K58","notation":["37K58"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational principles and methods for infinite-dimensional Hamiltonian and Lagrangian systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K60","notation":["37K60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattice dynamics; integrable lattice equations"},"scopeNote":{"en":["See also 37L60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37K99","notation":["37K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Kxx","notation":["37Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite-dimensional dissipative dynamical systems"},"scopeNote":{"en":["See also 35Bxx, 35Qxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L05","notation":["37L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L10","notation":["37L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L15","notation":["37L15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability problems for infinite-dimensional dissipative dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L20","notation":["37L20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symmetries of infinite-dimensional dissipative dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L25","notation":["37L25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L30","notation":["37L30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite-dimensional dissipative dynamical systems–attractors and their dimensions, Lyapunov exponents"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L40","notation":["37L40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Invariant measures for infinite-dimensional dissipative dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L45","notation":["37L45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperbolicity; Lyapunov functions for infinite-dimensional dissipative dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L50","notation":["37L50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncompact semigroups; dispersive equations; perturbations of infinite-dimensional dissipative dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L55","notation":["37L55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite-dimensional random dynamical systems; stochastic equations"},"scopeNote":{"en":["See also 35R60, 60H10, 60H15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L60","notation":["37L60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattice dynamics and infinite-dimensional dissipative dynamical systems"},"scopeNote":{"en":["See also 37K60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L65","notation":["37L65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37L99","notation":["37L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Lxx","notation":["37Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Mxx","notation":["37Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Approximation methods and numerical treatment of dynamical systems"},"scopeNote":{"en":["For numerical analysis, see also 65Pxx; for software etc., see 37-04"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37M05","notation":["37M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Simulation of dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Mxx","notation":["37Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37M10","notation":["37M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Time series analysis of dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Mxx","notation":["37Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37M15","notation":["37M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Mxx","notation":["37Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37M20","notation":["37M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for bifurcation problems in dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Mxx","notation":["37Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37M21","notation":["37M21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for invariant manifolds of dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Mxx","notation":["37Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37M22","notation":["37M22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for attractors of dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Mxx","notation":["37Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37M25","notation":["37M25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Mxx","notation":["37Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37M99","notation":["37M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Mxx","notation":["37Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Nxx","notation":["37Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37N05","notation":["37N05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems in classical and celestial mechanics"},"scopeNote":{"en":["See mainly 70Fxx, 70Hxx, 70Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Nxx","notation":["37Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37N10","notation":["37N10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems in fluid mechanics, oceanography and meteorology"},"scopeNote":{"en":["See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Nxx","notation":["37Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37N15","notation":["37N15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems in solid mechanics"},"scopeNote":{"en":["See mainly 74Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Nxx","notation":["37Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37N20","notation":["37N20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Nxx","notation":["37Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37N25","notation":["37N25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems in biology"},"scopeNote":{"en":["See also 92-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Nxx","notation":["37Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37N30","notation":["37N30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems in numerical analysis"},"scopeNote":{"en":["See also 65-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Nxx","notation":["37Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37N35","notation":["37N35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems in control"},"scopeNote":{"en":["See also 93-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Nxx","notation":["37Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37N40","notation":["37N40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems in optimization and economics"},"scopeNote":{"en":["See also 90-XX, 91-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Nxx","notation":["37Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37N99","notation":["37N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Nxx","notation":["37Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic and non-Archimedean dynamical systems"},"scopeNote":{"en":["See also 11S82, 37A45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37-XX","notation":["37-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37P05","notation":["37P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37P10","notation":["37P10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic and non-Archimedean dynamical systems involving analytic and meromorphic maps"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37P15","notation":["37P15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems over global ground fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37P20","notation":["37P20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems over non-Archimedean local ground fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37P25","notation":["37P25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems over finite ground fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37P30","notation":["37P30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems"},"scopeNote":{"en":["See also 11G50, 14G40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37P35","notation":["37P35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic properties of periodic points"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37P40","notation":["37P40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Non-Archimedean Fatou and Julia sets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37P45","notation":["37P45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Families and moduli spaces in arithmetic and non-Archimedean dynamical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37P50","notation":["37P50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems on Berkovich spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37P55","notation":["37P55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic dynamics on general algebraic varieties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/37P99","notation":["37P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/37Pxx","notation":["37Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39-XX","notation":["39-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Difference and functional equations"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39-00","notation":["39-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to difference and functional equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39-XX","notation":["39-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39-01","notation":["39-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39-XX","notation":["39-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39-02","notation":["39-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to difference and functional equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39-XX","notation":["39-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39-03","notation":["39-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of difference and functional equations"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39-XX","notation":["39-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39-04","notation":["39-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to difference and functional equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39-XX","notation":["39-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39-06","notation":["39-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to difference and functional equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39-XX","notation":["39-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39-08","notation":["39-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to difference and functional equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39-XX","notation":["39-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39-11","notation":["39-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to difference and functional equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39-XX","notation":["39-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Difference equations"},"scopeNote":{"en":["For dynamic equations on time scales, see 34N05; for dynamical systems, see 37-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39-XX","notation":["39-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A05","notation":["39A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A06","notation":["39A06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A10","notation":["39A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Additive difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A12","notation":["39A12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discrete version of topics in analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A13","notation":["39A13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Difference equations, scaling (q-differences)"},"scopeNote":{"en":["See also 33Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A14","notation":["39A14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partial difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A20","notation":["39A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiplicative and other generalized difference equations, e.g., of Lyness type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A21","notation":["39A21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Oscillation theory for difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A22","notation":["39A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Growth, boundedness, comparison of solutions to difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A23","notation":["39A23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Periodic solutions of difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A24","notation":["39A24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Almost periodic solutions of difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A26","notation":["39A26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A27","notation":["39A27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems for difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A28","notation":["39A28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcation theory for difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A30","notation":["39A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability theory for difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A33","notation":["39A33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chaotic behavior of solutions of difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A35","notation":["39A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integrable difference and lattice equations; integrability tests"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A45","notation":["39A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Difference equations in the complex domain"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A50","notation":["39A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A60","notation":["39A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of difference equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A70","notation":["39A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Difference operators"},"scopeNote":{"en":["See also 47B39"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39A99","notation":["39A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Axx","notation":["39Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39Bxx","notation":["39Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional equations and inequalities"},"scopeNote":{"en":["See also 30D05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39-XX","notation":["39-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39B05","notation":["39B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of functional equations and inequalities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Bxx","notation":["39Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39B12","notation":["39B12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Iteration theory, iterative and composite equations"},"scopeNote":{"en":["See also 26A18, 30D05, 37-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Bxx","notation":["39Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39B22","notation":["39B22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional equations for real functions"},"scopeNote":{"en":["See also 26A51, 26B25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Bxx","notation":["39Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39B32","notation":["39B32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional equations for complex functions"},"scopeNote":{"en":["See also 30D05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Bxx","notation":["39Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39B42","notation":["39B42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matrix and operator functional equations"},"scopeNote":{"en":["See also 47Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Bxx","notation":["39Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39B52","notation":["39B52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional equations for functions with more general domains and/or ranges"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Bxx","notation":["39Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39B55","notation":["39B55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orthogonal additivity and other conditional functional equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Bxx","notation":["39Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39B62","notation":["39B62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional inequalities, including subadditivity, convexity, etc."},"scopeNote":{"en":["See also 26A51, 26B25, 26Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Bxx","notation":["39Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39B72","notation":["39B72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Systems of functional equations and inequalities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Bxx","notation":["39Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39B82","notation":["39B82"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability, separation, extension, and related topics for functional equations"},"scopeNote":{"en":["See also 46A22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Bxx","notation":["39Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/39B99","notation":["39B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/39Bxx","notation":["39Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sequences, series, summability"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40-00","notation":["40-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to sequences, series, summability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40-01","notation":["40-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to sequences, series, summability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40-02","notation":["40-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to sequences, series, summability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40-03","notation":["40-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of sequences, series, summability"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40-04","notation":["40-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to sequences, series, summability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40-06","notation":["40-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to sequences, series, summability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40-08","notation":["40-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to sequences, series, summability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40-11","notation":["40-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to sequences, series, summability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40Axx","notation":["40Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convergence and divergence of infinite limiting processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40A05","notation":["40A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convergence and divergence of series and sequences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Axx","notation":["40Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40A10","notation":["40A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convergence and divergence of integrals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Axx","notation":["40Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40A15","notation":["40A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convergence and divergence of continued fractions"},"scopeNote":{"en":["See also 30B70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Axx","notation":["40Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40A20","notation":["40A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convergence and divergence of infinite products"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Axx","notation":["40Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40A25","notation":["40A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Approximation to limiting values (summation of series, etc.)"},"scopeNote":{"en":["For the Euler-Maclaurin summation formula, see 65B15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Axx","notation":["40Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40A30","notation":["40A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convergence and divergence of series and sequences of functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Axx","notation":["40Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40A35","notation":["40A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ideal and statistical convergence"},"scopeNote":{"en":["See also 40G15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Axx","notation":["40Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40A99","notation":["40A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Axx","notation":["40Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40Bxx","notation":["40Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiple sequences and series"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40B05","notation":["40B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiple sequences and series (should also be assigned at least one other classification number in this section)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Bxx","notation":["40Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40B99","notation":["40B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Bxx","notation":["40Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40Cxx","notation":["40Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General summability methods"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40C05","notation":["40C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matrix methods for summability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Cxx","notation":["40Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40C10","notation":["40C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral methods for summability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Cxx","notation":["40Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40C15","notation":["40C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Function-theoretic methods (including power series methods and semicontinuous methods) for summability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Cxx","notation":["40Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40C99","notation":["40C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Cxx","notation":["40Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40Dxx","notation":["40Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Direct theorems on summability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40-XX","notation":["40-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40D05","notation":["40D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theorems on summability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Dxx","notation":["40Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40D09","notation":["40D09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure of summability fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Dxx","notation":["40Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40D10","notation":["40D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Tauberian constants and oscillation limits in summability theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Dxx","notation":["40Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40D15","notation":["40D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convergence factors and summability factors"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Dxx","notation":["40Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40D20","notation":["40D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Summability and bounded fields of methods"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Dxx","notation":["40Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40D25","notation":["40D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inclusion and equivalence theorems in summability theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Dxx","notation":["40Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/40D99","notation":["40D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/40Dxx","notation":["40Dxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/42A24","notation":["42A24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Summability and absolute summability of Fourier and trigonometric series"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A32","notation":["42A32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A38","notation":["42A38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A45","notation":["42A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multipliers in one variable harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A50","notation":["42A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Conjugate functions, conjugate series, singular integrals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A55","notation":["42A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lacunary series of trigonometric and other functions; Riesz products"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A61","notation":["42A61"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probabilistic methods for one variable harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A63","notation":["42A63"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A65","notation":["42A65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Completeness of sets of functions in one variable harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A70","notation":["42A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Trigonometric moment problems in one variable harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A75","notation":["42A75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical almost periodic functions, mean periodic functions"},"scopeNote":{"en":["See also 43A60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A82","notation":["42A82"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Positive definite functions in one variable harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A85","notation":["42A85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convolution, factorization for one variable harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42A99","notation":["42A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Axx","notation":["42Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42Bxx","notation":["42Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic analysis in several variables"},"scopeNote":{"en":["For automorphic theory, see mainly 11F30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42-XX","notation":["42-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42B05","notation":["42B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fourier series and coefficients in several variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Bxx","notation":["42Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42B08","notation":["42B08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Summability in several variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Bxx","notation":["42Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42B10","notation":["42B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Bxx","notation":["42Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42B15","notation":["42B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multipliers for harmonic analysis in several variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Bxx","notation":["42Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42B20","notation":["42B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular and oscillatory integrals (Calderón-Zygmund, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Bxx","notation":["42Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42B25","notation":["42B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Maximal functions, Littlewood-Paley theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Bxx","notation":["42Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42B30","notation":["42B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"H p -spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Bxx","notation":["42Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42B35","notation":["42B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Function spaces arising in harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Bxx","notation":["42Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42B37","notation":["42B37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic analysis and PDEs"},"scopeNote":{"en":["See also 35-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Bxx","notation":["42Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42B99","notation":["42B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Bxx","notation":["42Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42Cxx","notation":["42Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nontrigonometric harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42-XX","notation":["42-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42C05","notation":["42C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis"},"scopeNote":{"en":["See also 33C45, 33C50, 33D45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Cxx","notation":["42Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42C10","notation":["42C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Cxx","notation":["42Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42C15","notation":["42C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General harmonic expansions, frames"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Cxx","notation":["42Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42C20","notation":["42C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other transformations of harmonic type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Cxx","notation":["42Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42C25","notation":["42C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Uniqueness and localization for orthogonal series"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Cxx","notation":["42Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42C30","notation":["42C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Completeness of sets of functions in nontrigonometric harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Cxx","notation":["42Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42C40","notation":["42C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nontrigonometric harmonic analysis involving wavelets and other special systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Cxx","notation":["42Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/42C99","notation":["42C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/42Cxx","notation":["42Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43-XX","notation":["43-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract harmonic analysis"},"scopeNote":{"en":["For other analysis on topological and Lie groups, see 22Exx"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43-00","notation":["43-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to abstract harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43-XX","notation":["43-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43-01","notation":["43-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to abstract harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43-XX","notation":["43-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43-02","notation":["43-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to abstract harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43-XX","notation":["43-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43-03","notation":["43-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of abstract harmonic analysis"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43-XX","notation":["43-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43-04","notation":["43-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to abstract harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43-XX","notation":["43-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43-06","notation":["43-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to abstract harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43-XX","notation":["43-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43-08","notation":["43-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to abstract harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43-XX","notation":["43-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43-11","notation":["43-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to abstract harmonic analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43-XX","notation":["43-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract harmonic analysis"},"scopeNote":{"en":["For other analysis on topological and Lie groups, see 22Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43-XX","notation":["43-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A05","notation":["43A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measures on groups and semigroups, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A07","notation":["43A07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Means on groups, semigroups, etc.; amenable groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A10","notation":["43A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measure algebras on groups, semigroups, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A15","notation":["43A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lp -spaces and other function spaces on groups, semigroups, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A17","notation":["43A17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis on ordered groups, H p -theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A20","notation":["43A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"L1 -algebras on groups, semigroups, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A22","notation":["43A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homomorphisms and multipliers of function spaces on groups, semigroups, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A25","notation":["43A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A30","notation":["43A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A32","notation":["43A32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other transforms and operators of Fourier type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A35","notation":["43A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Positive definite functions on groups, semigroups, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A40","notation":["43A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Character groups and dual objects"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A45","notation":["43A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral synthesis on groups, semigroups, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A46","notation":["43A46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A50","notation":["43A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convergence of Fourier series and of inverse transforms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A55","notation":["43A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Summability methods on groups, semigroups, etc."},"scopeNote":{"en":["See also 40J05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A60","notation":["43A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A62","notation":["43A62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic analysis on hypergroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A65","notation":["43A65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)"},"scopeNote":{"en":["See also 22A10, 22A20, 22Dxx, 22E45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A70","notation":["43A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis on specific locally compact and other abelian groups"},"scopeNote":{"en":["See also 11R56, 22B05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A75","notation":["43A75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic analysis on specific compact groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A77","notation":["43A77"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic analysis on general compact groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A80","notation":["43A80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis on other specific Lie groups"},"scopeNote":{"en":["See also 22Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A85","notation":["43A85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic analysis on homogeneous spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A90","notation":["43A90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic analysis and spherical functions"},"scopeNote":{"en":["See also 22E45, 22E46, 33C55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A95","notation":["43A95"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categorical methods for abstract harmonic analysis"},"scopeNote":{"en":["See also 46Mxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/43A99","notation":["43A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/43Axx","notation":["43Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44-XX","notation":["44-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral transforms, operational calculus"},"scopeNote":{"en":["For fractional derivatives and integrals, see 26A33; for Fourier transforms, see 42A38, 42B10; for integral transforms in distribution spaces, see 46F12; for numerical methods, see 65R10"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/44-01","notation":["44-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral transforms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44-XX","notation":["44-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44-02","notation":["44-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to integral transforms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44-XX","notation":["44-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44-03","notation":["44-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of integral transforms"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44-XX","notation":["44-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44-04","notation":["44-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to integral transforms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44-XX","notation":["44-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44-06","notation":["44-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to integral transforms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44-XX","notation":["44-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44-11","notation":["44-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to integral transforms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44-XX","notation":["44-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral transforms, operational calculus"},"scopeNote":{"en":["For fractional derivatives and integrals, see 26A33; for Fourier transforms, see 42A38, 42B10; for integral transforms in distribution spaces, see 46F12; for numerical methods, see 65R10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44-XX","notation":["44-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44A05","notation":["44A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General integral transforms"},"scopeNote":{"en":["See also 42A38"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44A10","notation":["44A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Laplace transform"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44A12","notation":["44A12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Radon transform"},"scopeNote":{"en":["See also 92C55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44A15","notation":["44A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special integral transforms (Legendre, Hilbert, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44A20","notation":["44A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral transforms of special functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44A30","notation":["44A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiple integral transforms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44A35","notation":["44A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convolution as an integral transform"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44A40","notation":["44A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Calculus of Mikusiński and other operational calculi"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44A45","notation":["44A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical operational calculus"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44A55","notation":["44A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discrete operational calculus"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44A60","notation":["44A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Moment problems"},"scopeNote":{"en":["For trigonometric moment problems, see 42A70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/44A99","notation":["44A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/44Axx","notation":["44Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral equations"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45-00","notation":["45-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45-01","notation":["45-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45-02","notation":["45-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45-03","notation":["45-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of integral equations"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45-04","notation":["45-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45-06","notation":["45-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45-11","notation":["45-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Axx","notation":["45Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45A05","notation":["45A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Axx","notation":["45Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45A99","notation":["45A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Axx","notation":["45Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Bxx","notation":["45Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fredholm integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45B05","notation":["45B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fredholm integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Bxx","notation":["45Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45B99","notation":["45B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Bxx","notation":["45Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Cxx","notation":["45Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Eigenvalue problems for integral equations"},"scopeNote":{"en":["See also 34Lxx, 35Pxx, 45P05, 47A75"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45C05","notation":["45C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Eigenvalue problems for integral equations"},"scopeNote":{"en":["See also 34Lxx, 35Pxx, 45P05, 47A75"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Cxx","notation":["45Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45C99","notation":["45C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Cxx","notation":["45Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Dxx","notation":["45Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Volterra integral equations"},"scopeNote":{"en":["See also 34A12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45D05","notation":["45D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Volterra integral equations"},"scopeNote":{"en":["See also 34A12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Dxx","notation":["45Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45D99","notation":["45D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Dxx","notation":["45Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Exx","notation":["45Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular integral equations"},"scopeNote":{"en":["See also 30E20, 30E25, 44A15, 44A35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45E05","notation":["45E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral equations with kernels of Cauchy type"},"scopeNote":{"en":["See also 35J15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Exx","notation":["45Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45E10","notation":["45E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)"},"scopeNote":{"en":["See also 47B35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Exx","notation":["45Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45E99","notation":["45E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Exx","notation":["45Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Fxx","notation":["45Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Systems of linear integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45F05","notation":["45F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Systems of nonsingular linear integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Fxx","notation":["45Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45F10","notation":["45F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dual, triple, etc., integral and series equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Fxx","notation":["45Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45F15","notation":["45F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Systems of singular linear integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Fxx","notation":["45Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45F99","notation":["45F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Fxx","notation":["45Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Gxx","notation":["45Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear integral equations"},"scopeNote":{"en":["See also 47H30, 47Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45G05","notation":["45G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular nonlinear integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Gxx","notation":["45Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45G10","notation":["45G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other nonlinear integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Gxx","notation":["45Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45G15","notation":["45G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Systems of nonlinear integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Gxx","notation":["45Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45G99","notation":["45G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Gxx","notation":["45Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Hxx","notation":["45Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral equations with miscellaneous special kernels"},"scopeNote":{"en":["See also 44A15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45H05","notation":["45H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral equations with miscellaneous special kernels"},"scopeNote":{"en":["See also 44A15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Hxx","notation":["45Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45H99","notation":["45H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Hxx","notation":["45Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Jxx","notation":["45Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integro-ordinary differential equations"},"scopeNote":{"en":["See also 34K05, 34K30, 47G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45J05","notation":["45J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integro-ordinary differential equations"},"scopeNote":{"en":["See also 34K05, 34K30, 47G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Jxx","notation":["45Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45J99","notation":["45J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Jxx","notation":["45Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Kxx","notation":["45Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integro-partial differential equations"},"scopeNote":{"en":["See also 34K30, 35R09, 35R10, 47G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45K05","notation":["45K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integro-partial differential equations"},"scopeNote":{"en":["See also 34K30, 35R09, 35R10, 47G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Kxx","notation":["45Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45K99","notation":["45K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Kxx","notation":["45Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Lxx","notation":["45Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theoretical approximation of solutions to integral equations"},"scopeNote":{"en":["For numerical analysis, see 65Rxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45L05","notation":["45L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theoretical approximation of solutions to integral equations"},"scopeNote":{"en":["For numerical analysis, see 65Rxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Lxx","notation":["45Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45L99","notation":["45L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Lxx","notation":["45Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Mxx","notation":["45Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Qualitative behavior of solutions to integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45M05","notation":["45M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotics of solutions to integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Mxx","notation":["45Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45M10","notation":["45M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability theory for integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Mxx","notation":["45Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45M15","notation":["45M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Periodic solutions of integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Mxx","notation":["45Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45M20","notation":["45M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Positive solutions of integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Mxx","notation":["45Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45M99","notation":["45M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Mxx","notation":["45Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Nxx","notation":["45Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract integral equations, integral equations in abstract spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45N05","notation":["45N05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract integral equations, integral equations in abstract spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Nxx","notation":["45Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45N99","notation":["45N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Nxx","notation":["45Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Pxx","notation":["45Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral operators"},"scopeNote":{"en":["See also 47B38, 47G10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45P05","notation":["45P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral operators"},"scopeNote":{"en":["See also 47B38, 47G10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Pxx","notation":["45Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45P99","notation":["45P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Pxx","notation":["45Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Qxx","notation":["45Qxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems for integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Q05","notation":["45Q05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems for integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Qxx","notation":["45Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Q99","notation":["45Q99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Qxx","notation":["45Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45Rxx","notation":["45Rxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random integral equations"},"scopeNote":{"en":["See also 60H20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45-XX","notation":["45-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45R05","notation":["45R05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random integral equations"},"scopeNote":{"en":["See also 60H20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Rxx","notation":["45Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/45R99","notation":["45R99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/45Rxx","notation":["45Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional analysis"},"scopeNote":{"en":["For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46-00","notation":["46-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functional analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46-01","notation":["46-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46-02","notation":["46-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to functional analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46-03","notation":["46-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of functional analysis"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46-04","notation":["46-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to functional analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46-06","notation":["46-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to functional analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46-08","notation":["46-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to functional analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46-11","notation":["46-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to functional analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological linear spaces and related structures"},"scopeNote":{"en":["For function spaces, see 46Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A03","notation":["46A03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of locally convex spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A04","notation":["46A04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Locally convex Fréchet spaces and (DF)-spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A08","notation":["46A08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Barrelled spaces, bornological spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A11","notation":["46A11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A13","notation":["46A13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces defined by inductive or projective limits (LB, LF, etc.)"},"scopeNote":{"en":["See also 46M40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A16","notation":["46A16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A17","notation":["46A17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bornologies and related structures; Mackey convergence, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A19","notation":["46A19"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than R, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A20","notation":["46A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Duality theory for topological vector spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A22","notation":["46A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theorems of Hahn-Banach type; extension and lifting of functionals and operators"},"scopeNote":{"en":["See also 46M10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A25","notation":["46A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Reflexivity and semi-reflexivity"},"scopeNote":{"en":["See also 46B10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A30","notation":["46A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Open mapping and closed graph theorems; completeness (including B-, Br -completeness)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A32","notation":["46A32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces of linear operators; topological tensor products; approximation properties"},"scopeNote":{"en":["See also 46B28, 46M05, 47L05, 47L20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A35","notation":["46A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Summability and bases in topological vector spaces"},"scopeNote":{"en":["See also 46B15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A40","notation":["46A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered topological linear spaces, vector lattices"},"scopeNote":{"en":["See also 06F20, 46B40, 46B42"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A45","notation":["46A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sequence spaces (including Köthe sequence spaces)"},"scopeNote":{"en":["See also 46B45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A50","notation":["46A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compactness in topological linear spaces; angelic spaces, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A55","notation":["46A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convex sets in topological linear spaces; Choquet theory"},"scopeNote":{"en":["See also 52A07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A61","notation":["46A61"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graded Fréchet spaces and tame operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A63","notation":["46A63"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological invariants ((DN), (Ω), etc.) for locally convex spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A70","notation":["46A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A80","notation":["46A80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modular spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46A99","notation":["46A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Axx","notation":["46Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Normed linear spaces and Banach spaces; Banach lattices"},"scopeNote":{"en":["For function spaces, see 46Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B03","notation":["46B03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Isomorphic theory (including renorming) of Banach spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B04","notation":["46B04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Isometric theory of Banach spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B06","notation":["46B06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic theory of Banach spaces"},"scopeNote":{"en":["See also 52A23"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B07","notation":["46B07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local theory of Banach spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B08","notation":["46B08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ultraproduct techniques in Banach space theory"},"scopeNote":{"en":["See also 46M07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B09","notation":["46B09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probabilistic methods in Banach space theory"},"scopeNote":{"en":["See also 60Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B10","notation":["46B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Duality and reflexivity in normed linear and Banach spaces"},"scopeNote":{"en":["See also 46A25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B15","notation":["46B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces"},"scopeNote":{"en":["See also 46A35, 42C15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B20","notation":["46B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometry and structure of normed linear spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B22","notation":["46B22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Radon-Nikodým, Kreı̆n-Milman and related properties"},"scopeNote":{"en":["See also 46G10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B25","notation":["46B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical Banach spaces in the general theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B26","notation":["46B26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonseparable Banach spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B28","notation":["46B28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces of operators; tensor products; approximation properties"},"scopeNote":{"en":["See also 46A32, 46M05, 47L05, 47L20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B40","notation":["46B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered normed spaces"},"scopeNote":{"en":["See also 46A40, 46B42"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B42","notation":["46B42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Banach lattices"},"scopeNote":{"en":["See also 46A40, 46B40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B45","notation":["46B45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Banach sequence spaces"},"scopeNote":{"en":["See also 46A45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B50","notation":["46B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compactness in Banach (or normed) spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B70","notation":["46B70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Interpolation between normed linear spaces"},"scopeNote":{"en":["See also 46M35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B80","notation":["46B80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear classification of Banach spaces; nonlinear quotients"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B85","notation":["46B85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science"},"scopeNote":{"en":["See also 05C12, 68Rxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B87","notation":["46B87"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lineability in functional analysis"},"scopeNote":{"en":["See also 15A03"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46B99","notation":["46B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Bxx","notation":["46Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Cxx","notation":["46Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inner product spaces and their generalizations, Hilbert spaces"},"scopeNote":{"en":["For function spaces, see 46Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46C05","notation":["46C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Cxx","notation":["46Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46C07","notation":["46C07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)"},"scopeNote":{"en":["See also 46B70, 46M35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Cxx","notation":["46Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46C15","notation":["46C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Characterizations of Hilbert spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Cxx","notation":["46Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46C20","notation":["46C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces with indefinite inner product (Kreı̆n spaces, Pontryagin spaces, etc.)"},"scopeNote":{"en":["See also 47B50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Cxx","notation":["46Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46C50","notation":["46C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of inner products (semi-inner products, partial inner products, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Cxx","notation":["46Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46C99","notation":["46C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Cxx","notation":["46Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear function spaces and their duals"},"scopeNote":{"en":["See also 30H05, 32A38, 46F05; For function algebras, see 46J10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E05","notation":["46E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattices of continuous, differentiable or analytic functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E10","notation":["46E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological linear spaces of continuous, differentiable or analytic functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E15","notation":["46E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Banach spaces of continuous, differentiable or analytic functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E20","notation":["46E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hilbert spaces of continuous, differentiable or analytic functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E22","notation":["46E22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)"},"scopeNote":{"en":["See also 47B32"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E25","notation":["46E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rings and algebras of continuous, differentiable or analytic functions"},"scopeNote":{"en":["For Banach function algebras, see 46J10, 46J15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E27","notation":["46E27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces of measures"},"scopeNote":{"en":["See also 28A33, 46Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E30","notation":["46E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces of measurable functions (Lp -spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E35","notation":["46E35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E36","notation":["46E36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E39","notation":["46E39"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sobolev (and similar kinds of) spaces of functions of discrete variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E40","notation":["46E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces of vector- and operator-valued functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E50","notation":["46E50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces of differentiable or holomorphic functions on infinite-dimensional spaces"},"scopeNote":{"en":["See also 46G20, 46G25, 47H60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46E99","notation":["46E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Exx","notation":["46Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Fxx","notation":["46Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distributions, generalized functions, distribution spaces"},"scopeNote":{"en":["See also 46T30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46F05","notation":["46F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological linear spaces of test functions, distributions and ultradistributions"},"scopeNote":{"en":["See also 46E10, 46E35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Fxx","notation":["46Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46F10","notation":["46F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operations with distributions and generalized functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Fxx","notation":["46Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46F12","notation":["46F12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral transforms in distribution spaces"},"scopeNote":{"en":["See also 42-XX, 44-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Fxx","notation":["46Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46F15","notation":["46F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperfunctions, analytic functionals"},"scopeNote":{"en":["See also 32A25, 32A45, 32C35, 58J15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Fxx","notation":["46Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46F20","notation":["46F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distributions and ultradistributions as boundary values of analytic functions"},"scopeNote":{"en":["See also 30D40, 30E25, 32A40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Fxx","notation":["46Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46F25","notation":["46F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distributions on infinite-dimensional spaces"},"scopeNote":{"en":["See also 58C35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Fxx","notation":["46Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46F30","notation":["46F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Fxx","notation":["46Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46F99","notation":["46F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Fxx","notation":["46Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Gxx","notation":["46Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measures, integration, derivative, holomorphy (all involving infinitedimensional spaces)"},"scopeNote":{"en":["See also 28-XX, 46Txx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46G05","notation":["46G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Derivatives of functions in infinite-dimensional spaces"},"scopeNote":{"en":["See also 46T20, 58C20, 58C25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Gxx","notation":["46Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46G10","notation":["46G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vector-valued measures and integration"},"scopeNote":{"en":["See also 28Bxx, 46B22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Gxx","notation":["46Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46G12","notation":["46G12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measures and integration on abstract linear spaces"},"scopeNote":{"en":["See also 28C20, 46T12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Gxx","notation":["46Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46G15","notation":["46G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional analytic lifting theory"},"scopeNote":{"en":["See also 28A51"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Gxx","notation":["46Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46G20","notation":["46G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite-dimensional holomorphy"},"scopeNote":{"en":["See also 32-XX, 46E50, 46T25, 58B12, 58C10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Gxx","notation":["46Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46G25","notation":["46G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"(Spaces of) multilinear mappings, polynomials"},"scopeNote":{"en":["See also 46E50, 46G20, 47H60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Gxx","notation":["46Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46G99","notation":["46G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Gxx","notation":["46Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Hxx","notation":["46Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological algebras, normed rings and algebras, Banach algebras"},"scopeNote":{"en":["For group algebras, convolution algebras and measure algebras, see 43A10, 43A20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46H05","notation":["46H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of topological algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Hxx","notation":["46Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46H10","notation":["46H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ideals and subalgebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Hxx","notation":["46Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46H15","notation":["46H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of topological algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Hxx","notation":["46Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46H20","notation":["46H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure, classification of topological algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Hxx","notation":["46Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46H25","notation":["46H25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Hxx","notation":["46Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46H30","notation":["46H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional calculus in topological algebras"},"scopeNote":{"en":["See also 47A60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Hxx","notation":["46Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46H35","notation":["46H35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological algebras of operators"},"scopeNote":{"en":["See mainly 47Lxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Hxx","notation":["46Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46H40","notation":["46H40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automatic continuity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Hxx","notation":["46Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46H70","notation":["46H70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonassociative topological algebras"},"scopeNote":{"en":["See also 46K70, 46L70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Hxx","notation":["46Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46H99","notation":["46H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Hxx","notation":["46Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Jxx","notation":["46Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutative Banach algebras and commutative topological algebras"},"scopeNote":{"en":["See also 46E25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46J05","notation":["46J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of commutative topological algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Jxx","notation":["46Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46J10","notation":["46J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Banach algebras of continuous functions, function algebras"},"scopeNote":{"en":["See also 46E25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Jxx","notation":["46Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46J15","notation":["46J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Banach algebras of differentiable or analytic functions, H p -spaces"},"scopeNote":{"en":["See also 30H10, 32A35, 32A37, 32A38, 42B30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Jxx","notation":["46Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46J20","notation":["46J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ideals, maximal ideals, boundaries"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Jxx","notation":["46Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46J25","notation":["46J25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of commutative topological algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Jxx","notation":["46Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46J30","notation":["46J30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subalgebras of commutative topological algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Jxx","notation":["46Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46J40","notation":["46J40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure and classification of commutative topological algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Jxx","notation":["46Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46J45","notation":["46J45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Radical Banach algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Jxx","notation":["46Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46J99","notation":["46J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Jxx","notation":["46Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Kxx","notation":["46Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological (rings and) algebras with an involution"},"scopeNote":{"en":["See also 16W10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46K05","notation":["46K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of topological algebras with involution"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Kxx","notation":["46Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46K10","notation":["46K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of topological algebras with involution"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Kxx","notation":["46Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46K15","notation":["46K15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hilbert algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Kxx","notation":["46Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46K50","notation":["46K50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonselfadjoint (sub)algebras in algebras with involution"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Kxx","notation":["46Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46K70","notation":["46K70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonassociative topological algebras with an involution"},"scopeNote":{"en":["See also 46H70, 46L70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Kxx","notation":["46Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46K99","notation":["46K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Kxx","notation":["46Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Selfadjoint operator algebras (C ∗ -algebras, von Neumann (W ∗ -) algebras, etc.)"},"scopeNote":{"en":["See also 22D25, 47Lxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L05","notation":["46L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of C ∗ -algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L06","notation":["46L06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Tensor products of C ∗ -algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L07","notation":["46L07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator spaces and completely bounded maps"},"scopeNote":{"en":["See also 47L25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L08","notation":["46L08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"C ∗ -modules"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L09","notation":["46L09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free products of C ∗ -algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L10","notation":["46L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of von Neumann algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L30","notation":["46L30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"States of selfadjoint operator algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L35","notation":["46L35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classifications of C ∗ -algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L36","notation":["46L36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classification of factors"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L37","notation":["46L37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subfactors and their classification"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L40","notation":["46L40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Automorphisms of selfadjoint operator algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L45","notation":["46L45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Decomposition theory for C ∗ -algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L51","notation":["46L51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative measure and integration"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L52","notation":["46L52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative function spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L53","notation":["46L53"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative probability and statistics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L54","notation":["46L54"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free probability and free operator algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L55","notation":["46L55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative dynamical systems"},"scopeNote":{"en":["See also 28Dxx, 37Kxx, 37Lxx, 37A55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L57","notation":["46L57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Derivations, dissipations and positive semigroups in C ∗ -algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L60","notation":["46L60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of selfadjoint operator algebras to physics"},"scopeNote":{"en":["See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L65","notation":["46L65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantizations, deformations for selfadjoint operator algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L67","notation":["46L67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum groups (operator algebraic aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L70","notation":["46L70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonassociative selfadjoint operator algebras"},"scopeNote":{"en":["See also 46H70, 46K70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L80","notation":["46L80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"K-theory and operator algebras (including cyclic theory)"},"scopeNote":{"en":["See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L85","notation":["46L85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative topology"},"scopeNote":{"en":["See also 58B32, 58B34, 58J22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L87","notation":["46L87"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative differential geometry"},"scopeNote":{"en":["See also 58B32, 58B34, 58J22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L89","notation":["46L89"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other “noncommutative” mathematics based on C ∗ -algebra theory"},"scopeNote":{"en":["See also 58B32, 58B34, 58J22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46L99","notation":["46L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Lxx","notation":["46Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Mxx","notation":["46Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methods of category theory in functional analysis"},"scopeNote":{"en":["See also 18-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46M05","notation":["46M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Tensor products in functional analysis"},"scopeNote":{"en":["See also 46A32, 46B28, 47A80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Mxx","notation":["46Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46M07","notation":["46M07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ultraproducts in functional analysis"},"scopeNote":{"en":["See also 46B08, 46S20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Mxx","notation":["46Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46M10","notation":["46M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Projective and injective objects in functional analysis"},"scopeNote":{"en":["See also 46A22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Mxx","notation":["46Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46M15","notation":["46M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categories, functors in functional analysis"},"scopeNote":{"en":["For K-theory, Ext, etc., see 19K33, 46L80, 46M18, 46M20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Mxx","notation":["46Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46M18","notation":["46M18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Mxx","notation":["46Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46M20","notation":["46M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)"},"scopeNote":{"en":["See also 14F06, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Mxx","notation":["46Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46M35","notation":["46M35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract interpolation of topological vector spaces"},"scopeNote":{"en":["See also 46B70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Mxx","notation":["46Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46M40","notation":["46M40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inductive and projective limits in functional analysis"},"scopeNote":{"en":["See also 46A13"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Mxx","notation":["46Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46M99","notation":["46M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Mxx","notation":["46Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Nxx","notation":["46Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Miscellaneous applications of functional analysis"},"scopeNote":{"en":["See also 47Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46N10","notation":["46N10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of functional analysis in optimization, convex analysis, mathematical programming, economics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Nxx","notation":["46Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46N20","notation":["46N20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of functional analysis to differential and integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Nxx","notation":["46Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46N30","notation":["46N30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of functional analysis in probability theory and statistics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Nxx","notation":["46Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46N40","notation":["46N40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of functional analysis in numerical analysis"},"scopeNote":{"en":["See also 65Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Nxx","notation":["46Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46N50","notation":["46N50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of functional analysis in quantum physics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Nxx","notation":["46Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46N55","notation":["46N55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of functional analysis in statistical physics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Nxx","notation":["46Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46N60","notation":["46N60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of functional analysis in biology and other sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Nxx","notation":["46Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46N99","notation":["46N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Nxx","notation":["46Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Sxx","notation":["46Sxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other (nonclassical) types of functional analysis"},"scopeNote":{"en":["See also 47Sxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46S05","notation":["46S05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quaternionic functional analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Sxx","notation":["46Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46S10","notation":["46S10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis"},"scopeNote":{"en":["See also 12J25, 32P05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Sxx","notation":["46Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46S20","notation":["46S20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonstandard functional analysis"},"scopeNote":{"en":["See also 03H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Sxx","notation":["46Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46S30","notation":["46S30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Constructive functional analysis"},"scopeNote":{"en":["See also 03F60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Sxx","notation":["46Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46S40","notation":["46S40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy functional analysis"},"scopeNote":{"en":["See also 03E72"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Sxx","notation":["46Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46S50","notation":["46S50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional analysis in probabilistic metric linear spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Sxx","notation":["46Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46S60","notation":["46S60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional analysis on superspaces (supermanifolds) or graded spaces"},"scopeNote":{"en":["See also 58A50, 58C50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Sxx","notation":["46Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46S99","notation":["46S99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Sxx","notation":["46Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46Txx","notation":["46Txx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear functional analysis"},"scopeNote":{"en":["See also 47Hxx, 47Jxx, 58Cxx, 58Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46-XX","notation":["46-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46T05","notation":["46T05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite-dimensional manifolds"},"scopeNote":{"en":["See also 53Axx, 57N20, 58Bxx, 58Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Txx","notation":["46Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46T10","notation":["46T10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Manifolds of mappings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Txx","notation":["46Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46T12","notation":["46T12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds"},"scopeNote":{"en":["See also 28Cxx, 46G12, 60-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Txx","notation":["46Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46T20","notation":["46T20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuous and differentiable maps in nonlinear functional analysis"},"scopeNote":{"en":["See also 46G05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Txx","notation":["46Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46T25","notation":["46T25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Holomorphic maps in nonlinear functional analysis"},"scopeNote":{"en":["See also 46G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Txx","notation":["46Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46T30","notation":["46T30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distributions and generalized functions on nonlinear spaces"},"scopeNote":{"en":["See also 46Fxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Txx","notation":["46Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/46T99","notation":["46T99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/46Txx","notation":["46Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator theory"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47-00","notation":["47-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to operator theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47-01","notation":["47-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47-02","notation":["47-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to operator theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47-03","notation":["47-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of operator theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47-04","notation":["47-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to operator theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47-06","notation":["47-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to operator theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47-08","notation":["47-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to operator theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47-11","notation":["47-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to operator theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of linear operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A05","notation":["47A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General (adjoints, conjugates, products, inverses, domains, ranges, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A06","notation":["47A06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear relations (multivalued linear operators)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A07","notation":["47A07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Forms (bilinear, sesquilinear, multilinear)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A08","notation":["47A08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator matrices"},"scopeNote":{"en":["See also 47A13"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A10","notation":["47A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectrum, resolvent"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A11","notation":["47A11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local spectral properties of linear operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A12","notation":["47A12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Numerical range, numerical radius"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A13","notation":["47A13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Several-variable operator theory (spectral, Fredholm, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A15","notation":["47A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Invariant subspaces of linear operators"},"scopeNote":{"en":["See also 47A46"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A16","notation":["47A16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cyclic vectors, hypercyclic and chaotic operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A20","notation":["47A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dilations, extensions, compressions of linear operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A25","notation":["47A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral sets of linear operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A30","notation":["47A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Norms (inequalities, more than one norm, etc.) of linear operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A35","notation":["47A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ergodic theory of linear operators"},"scopeNote":{"en":["See also 28Dxx, 37Axx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A40","notation":["47A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Scattering theory of linear operators"},"scopeNote":{"en":["See also 34L25, 35P25, 37K15, 58J50, 81Uxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A45","notation":["47A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Canonical models for contractions and nonselfadjoint linear operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A46","notation":["47A46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chains (nests) of projections or of invariant subspaces, integrals along chains, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A48","notation":["47A48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A50","notation":["47A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equations and inequalities involving linear operators, with vector unknowns"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A52","notation":["47A52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operators and ill-posed problems, regularization"},"scopeNote":{"en":["See also 35R25, 47J06, 65F22, 65J20, 65L08, 65M30, 65R30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A53","notation":["47A53"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"(Semi-) Fredholm operators; index theories"},"scopeNote":{"en":["See also 58B15, 58J20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A55","notation":["47A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perturbation theory of linear operators"},"scopeNote":{"en":["See also 47H14, 58J37, 70H09, 81Q15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A56","notation":["47A56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A57","notation":["47A57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operator methods in interpolation, moment and extension problems"},"scopeNote":{"en":["See also 30E05, 42A70, 42A82, 44A60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A58","notation":["47A58"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operator approximation theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A60","notation":["47A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional calculus for linear operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A62","notation":["47A62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equations involving linear operators, with operator unknowns"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A63","notation":["47A63"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operator inequalities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A64","notation":["47A64"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator means involving linear operators, shorted linear operators, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A65","notation":["47A65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Structure theory of linear operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A66","notation":["47A66"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal linear operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A67","notation":["47A67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representation theory of linear operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A68","notation":["47A68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A70","notation":["47A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"(Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A75","notation":["47A75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Eigenvalue problems for linear operators"},"scopeNote":{"en":["See also 47J10, 49R05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A80","notation":["47A80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Tensor products of linear operators"},"scopeNote":{"en":["See also 46M05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47A99","notation":["47A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Axx","notation":["47Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special classes of linear operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B01","notation":["47B01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operators on Banach spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B02","notation":["47B02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operators on Hilbert spaces (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B06","notation":["47B06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Riesz operators; eigenvalue distributions; approximation numbers, s-numbers, Kolmogorov numbers, entropy numbers, etc. of operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B07","notation":["47B07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operators defined by compactness properties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B10","notation":["47B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.)"},"scopeNote":{"en":["See also 47L20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B12","notation":["47B12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sectorial operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B13","notation":["47B13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cowen-Douglas operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B15","notation":["47B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hermitian and normal operators (spectral measures, functional calculus, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B20","notation":["47B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subnormal operators, hyponormal operators, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B25","notation":["47B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear symmetric and selfadjoint operators (unbounded)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B28","notation":["47B28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonselfadjoint operators"},"scopeNote":{"en":["See also 47A45, 81Q12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B32","notation":["47B32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)"},"scopeNote":{"en":["See also 46E22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B33","notation":["47B33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear composition operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B34","notation":["47B34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kernel operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B35","notation":["47B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Toeplitz operators, Hankel operators, Wiener-Hopf operators"},"scopeNote":{"en":["For other integral operators, see also 45P05, 47G10; See also 32A25, 32M15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B36","notation":["47B36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jacobi (tridiagonal) operators (matrices) and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B37","notation":["47B37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B38","notation":["47B38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operators on function spaces (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B39","notation":["47B39"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear difference operators"},"scopeNote":{"en":["See also 39A70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B40","notation":["47B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral operators, decomposable operators, well-bounded operators, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B44","notation":["47B44"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear accretive operators, dissipative operators, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B47","notation":["47B47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutators, derivations, elementary operators, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B48","notation":["47B48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operators on Banach algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B49","notation":["47B49"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transformers, preservers (linear operators on spaces of linear operators)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B50","notation":["47B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operators on spaces with an indefinite metric"},"scopeNote":{"en":["See also 46C20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B60","notation":["47B60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operators on ordered spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B65","notation":["47B65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Positive linear operators and order-bounded operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B80","notation":["47B80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random linear operators"},"scopeNote":{"en":["See also 47H40, 60H25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B90","notation":["47B90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator theory and harmonic analysis"},"scopeNote":{"en":["See also 42-XX, 43-XX, 44-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B91","notation":["47B91"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operators on complex function spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B92","notation":["47B92"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operators on real function spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B93","notation":["47B93"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operators arising in mathematical physics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47B99","notation":["47B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Bxx","notation":["47Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47Cxx","notation":["47Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Individual linear operators as elements of algebraic systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47C05","notation":["47C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operators in algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Cxx","notation":["47Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47C10","notation":["47C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operators in ∗ -algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Cxx","notation":["47Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47C15","notation":["47C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear operators in C ∗ - or von Neumann algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Cxx","notation":["47Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47C99","notation":["47C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Cxx","notation":["47Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47Dxx","notation":["47Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groups and semigroups of linear operators, their generalizations and applications"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47D03","notation":["47D03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groups and semigroups of linear operators"},"scopeNote":{"en":["See also 20M20; For nonlinear operators, see 47H20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Dxx","notation":["47Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47D06","notation":["47D06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"One-parameter semigroups and linear evolution equations"},"scopeNote":{"en":["See also 34G10, 34K30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Dxx","notation":["47Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47D07","notation":["47D07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Markov semigroups and applications to diffusion processes"},"scopeNote":{"en":["For Markov processes, see 60Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Dxx","notation":["47Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47D08","notation":["47D08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Schrödinger and Feynman-Kac semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Dxx","notation":["47Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47D09","notation":["47D09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator sine and cosine functions and higher-order Cauchy problems"},"scopeNote":{"en":["See also 34G10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Dxx","notation":["47Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47D60","notation":["47D60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"C-semigroups, regularized semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Dxx","notation":["47Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47D62","notation":["47D62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integrated semigroups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Dxx","notation":["47Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47D99","notation":["47D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Dxx","notation":["47Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47Exx","notation":["47Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential operators"},"scopeNote":{"en":["See also 34Bxx, 34Lxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47E05","notation":["47E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordinary differential operators (should also be assigned at least one other classification number in Section 47)"},"scopeNote":{"en":["See also 34Bxx, 34Lxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Exx","notation":["47Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47E07","notation":["47E07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional-differential and differential-difference operators"},"scopeNote":{"en":["See also 34K08"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Exx","notation":["47Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47E99","notation":["47E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Exx","notation":["47Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47Fxx","notation":["47Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partial differential operators"},"scopeNote":{"en":["See also 35Pxx, 58Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47F05","notation":["47F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partial differential operators (should also be assigned at least one other classification number in Section 47)"},"scopeNote":{"en":["See also 35Pxx, 58Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Fxx","notation":["47Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47F10","notation":["47F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic operators and their generalizations"},"scopeNote":{"en":["For elliptic complexes, see 58J10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Fxx","notation":["47Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47F99","notation":["47F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Fxx","notation":["47Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47Gxx","notation":["47Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral, integro-differential, and pseudodifferential operators"},"scopeNote":{"en":["See also 58Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47G10","notation":["47G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral operators"},"scopeNote":{"en":["See also 45P05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Gxx","notation":["47Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47G20","notation":["47G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integro-differential operators"},"scopeNote":{"en":["See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Gxx","notation":["47Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47G30","notation":["47G30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pseudodifferential operators"},"scopeNote":{"en":["See also 35Sxx, 58Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Gxx","notation":["47Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47G40","notation":["47G40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Potential operators"},"scopeNote":{"en":["See also 31-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Gxx","notation":["47Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47G99","notation":["47G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Gxx","notation":["47Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear operators and their properties"},"scopeNote":{"en":["For global and geometric aspects, see 49J53, 58-XX, especially 58Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H04","notation":["47H04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set-valued operators"},"scopeNote":{"en":["See also 28B20, 54C60, 58C06"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H05","notation":["47H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monotone operators and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H06","notation":["47H06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear accretive operators, dissipative operators, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H07","notation":["47H07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H08","notation":["47H08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measures of noncompactness and condensing mappings, K-set contractions, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H09","notation":["47H09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H10","notation":["47H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fixed-point theorems"},"scopeNote":{"en":["See also 37C25, 54H25, 55M20, 58C30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H11","notation":["47H11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Degree theory for nonlinear operators"},"scopeNote":{"en":["See also 55M25, 58C30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H14","notation":["47H14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perturbations of nonlinear operators"},"scopeNote":{"en":["See also 47A55, 58J37, 70H09, 70K60, 81Q15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H20","notation":["47H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semigroups of nonlinear operators"},"scopeNote":{"en":["See also 37L05, 47J35, 54H15, 58D07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H25","notation":["47H25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear ergodic theorems"},"scopeNote":{"en":["See also 28Dxx, 37Axx, 47A35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H30","notation":["47H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Particular nonlinear operators (superposition, Hammerstein, Nemytskiı̆, Uryson, etc.)"},"scopeNote":{"en":["See also 45Gxx, 45P05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H40","notation":["47H40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random nonlinear operators"},"scopeNote":{"en":["See also 47B80, 60H25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H60","notation":["47H60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multilinear and polynomial operators"},"scopeNote":{"en":["See also 46G25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47H99","notation":["47H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Hxx","notation":["47Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equations and inequalities involving nonlinear operators"},"scopeNote":{"en":["See also 46Txx; For global and geometric aspects, see 58-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J05","notation":["47J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equations involving nonlinear operators (general)"},"scopeNote":{"en":["See also 47H10, 47J25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J06","notation":["47J06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear ill-posed problems"},"scopeNote":{"en":["See also 35R25, 47A52, 65F22, 65J20, 65L08, 65M30, 65R30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J07","notation":["47J07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract inverse mapping and implicit function theorems involving nonlinear operators"},"scopeNote":{"en":["See also 46T20, 58C15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J10","notation":["47J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear spectral theory, nonlinear eigenvalue problems"},"scopeNote":{"en":["See also 49R05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J15","notation":["47J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract bifurcation theory involving nonlinear operators"},"scopeNote":{"en":["See also 34C23, 37Gxx, 58E07, 58E09"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J20","notation":["47J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational and other types of inequalities involving nonlinear operators (general)"},"scopeNote":{"en":["See also 49J40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J22","notation":["47J22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational and other types of inclusions"},"scopeNote":{"en":["See also 34A60, 49J21, 49K21"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J25","notation":["47J25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Iterative procedures involving nonlinear operators"},"scopeNote":{"en":["See also 47J26, 65J15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J26","notation":["47J26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fixed-point iterations"},"scopeNote":{"en":["See also 47J25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J30","notation":["47J30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational methods involving nonlinear operators"},"scopeNote":{"en":["See also 58Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J35","notation":["47J35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear evolution equations"},"scopeNote":{"en":["See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J40","notation":["47J40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equations with nonlinear hysteresis operators"},"scopeNote":{"en":["See also 34C55, 74N30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47J99","notation":["47J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Jxx","notation":["47Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear spaces and algebras of operators"},"scopeNote":{"en":["See also 46Lxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L05","notation":["47L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear spaces of operators"},"scopeNote":{"en":["See also 46A32, 46B28"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L07","notation":["47L07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convex sets and cones of operators"},"scopeNote":{"en":["See also 46A55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L10","notation":["47L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebras of operators on Banach spaces and other topological linear spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L15","notation":["47L15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator algebras with symbol structure"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L20","notation":["47L20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator ideals"},"scopeNote":{"en":["See also 47B10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L22","notation":["47L22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ideals of polynomials and of multilinear mappings in operator theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L25","notation":["47L25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator spaces (= matricially normed spaces)"},"scopeNote":{"en":["See also 46L07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L30","notation":["47L30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract operator algebras on Hilbert spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L35","notation":["47L35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nest algebras, CSL algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L40","notation":["47L40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Limit algebras, subalgebras of C ∗ -algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L45","notation":["47L45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dual algebras; weakly closed singly generated operator algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L50","notation":["47L50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dual spaces of operator algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L55","notation":["47L55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representations of (nonselfadjoint) operator algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L60","notation":["47L60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebras of unbounded operators; partial algebras of operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L65","notation":["47L65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Crossed product algebras (analytic crossed products)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L70","notation":["47L70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonassociative nonselfadjoint operator algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L75","notation":["47L75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other nonselfadjoint operator algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L80","notation":["47L80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L90","notation":["47L90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of operator algebras to the sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47L99","notation":["47L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Lxx","notation":["47Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47Nxx","notation":["47Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Miscellaneous applications of operator theory"},"scopeNote":{"en":["See also 46Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47N10","notation":["47N10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of operator theory in optimization, convex analysis, mathematical programming, economics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Nxx","notation":["47Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47N20","notation":["47N20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of operator theory to differential and integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Nxx","notation":["47Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47N30","notation":["47N30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of operator theory in probability theory and statistics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Nxx","notation":["47Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47N40","notation":["47N40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of operator theory in numerical analysis"},"scopeNote":{"en":["See also 65Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Nxx","notation":["47Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47N50","notation":["47N50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of operator theory in the physical sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Nxx","notation":["47Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47N60","notation":["47N60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of operator theory in chemistry and life sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Nxx","notation":["47Nxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/47N99","notation":["47N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Nxx","notation":["47Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47Sxx","notation":["47Sxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other (nonclassical) types of operator theory"},"scopeNote":{"en":["See also 46Sxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47-XX","notation":["47-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47S05","notation":["47S05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quaternionic operator theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Sxx","notation":["47Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47S10","notation":["47S10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator theory over fields other than R, C or the quaternions; non-Archimedean operator theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Sxx","notation":["47Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47S20","notation":["47S20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonstandard operator theory"},"scopeNote":{"en":["See also 03H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Sxx","notation":["47Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47S30","notation":["47S30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Constructive operator theory"},"scopeNote":{"en":["See also 03F60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Sxx","notation":["47Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47S40","notation":["47S40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy operator theory"},"scopeNote":{"en":["See also 03E72"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Sxx","notation":["47Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47S50","notation":["47S50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator theory in probabilistic metric linear spaces"},"scopeNote":{"en":["See also 54E70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Sxx","notation":["47Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/47S99","notation":["47S99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/47Sxx","notation":["47Sxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/49-00","notation":["49-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to calculus of variations and optimal control"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49-XX","notation":["49-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49-01","notation":["49-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49-XX","notation":["49-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49-02","notation":["49-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49-XX","notation":["49-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49-03","notation":["49-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of calculus of variations and optimal control"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49-XX","notation":["49-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49-04","notation":["49-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to calculus of variations and optimal control"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49-XX","notation":["49-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49-06","notation":["49-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to calculus of variations and optimal control"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49-XX","notation":["49-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49-11","notation":["49-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to calculus of variations and optimal control"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49-XX","notation":["49-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence theories in calculus of variations and optimal control"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49-XX","notation":["49-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J05","notation":["49J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence theories for free problems in one independent variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J10","notation":["49J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence theories for free problems in two or more independent variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J15","notation":["49J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence theories for optimal control problems involving ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J20","notation":["49J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence theories for optimal control problems involving partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J21","notation":["49J21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence theories for optimal control problems involving relations other than differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J27","notation":["49J27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence theories for problems in abstract spaces"},"scopeNote":{"en":["See also 90C48, 93C25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J30","notation":["49J30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J35","notation":["49J35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence of solutions for minimax problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J40","notation":["49J40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational inequalities"},"scopeNote":{"en":["See also 47J20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J45","notation":["49J45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methods involving semicontinuity and convergence; relaxation"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J50","notation":["49J50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fréchet and Gateaux differentiability in optimization"},"scopeNote":{"en":["See also 46G05, 58C20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J52","notation":["49J52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonsmooth analysis"},"scopeNote":{"en":["See also 46G05, 58C50, 90C56"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J53","notation":["49J53"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set-valued and variational analysis"},"scopeNote":{"en":["See also 28B20, 47H04, 54C60, 58C06"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J55","notation":["49J55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence of optimal solutions to problems involving randomness"},"scopeNote":{"en":["See also 93E20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49J99","notation":["49J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Jxx","notation":["49Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49Kxx","notation":["49Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Optimality conditions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49-XX","notation":["49-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49K05","notation":["49K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Optimality conditions for free problems in one independent variable"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Kxx","notation":["49Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49K10","notation":["49K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Optimality conditions for free problems in two or more independent variables"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Kxx","notation":["49Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49K15","notation":["49K15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Optimality conditions for problems involving ordinary differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Kxx","notation":["49Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49K20","notation":["49K20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Optimality conditions for problems involving partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Kxx","notation":["49Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49K21","notation":["49K21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Optimality conditions for problems involving relations other than differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Kxx","notation":["49Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49K27","notation":["49K27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Optimality conditions for problems in abstract spaces"},"scopeNote":{"en":["See also 90C48, 93C25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Kxx","notation":["49Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49K30","notation":["49K30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Kxx","notation":["49Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/49K35","notation":["49K35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Optimality conditions for minimax problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Kxx","notation":["49Kxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/49N80","notation":["49N80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mean field games and control"},"scopeNote":{"en":["See also 91A16"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/49Nxx","notation":["49Nxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/51B15","notation":["51B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Laguerre geometries"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Bxx","notation":["51Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51B20","notation":["51B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Minkowski geometries in nonlinear incidence geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Bxx","notation":["51Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51B25","notation":["51B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lie geometries in nonlinear incidence geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Bxx","notation":["51Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51B99","notation":["51B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Bxx","notation":["51Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51Cxx","notation":["51Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ring geometry (Hjelmslev, Barbilian, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51-XX","notation":["51-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51C05","notation":["51C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ring geometry (Hjelmslev, Barbilian, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Cxx","notation":["51Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51C99","notation":["51C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Cxx","notation":["51Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51Dxx","notation":["51Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric closure systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51-XX","notation":["51-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51D05","notation":["51D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract (Maeda) geometries"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Dxx","notation":["51Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51D10","notation":["51D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract geometries with exchange axiom"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Dxx","notation":["51Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51D15","notation":["51D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract geometries with parallelism"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Dxx","notation":["51Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51D20","notation":["51D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial geometries and geometric closure systems"},"scopeNote":{"en":["See also 05B25, 05B35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Dxx","notation":["51Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51D25","notation":["51D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattices of subspaces and geometric closure systems"},"scopeNote":{"en":["See also 05B35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Dxx","notation":["51Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51D30","notation":["51D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuous geometries, geometric closure systems and related topics"},"scopeNote":{"en":["See also 06Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Dxx","notation":["51Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51D99","notation":["51D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Dxx","notation":["51Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite geometry and special incidence structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51-XX","notation":["51-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E05","notation":["51E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General block designs in finite geometry"},"scopeNote":{"en":["See also 05B05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E10","notation":["51E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Steiner systems in finite geometry"},"scopeNote":{"en":["See also 05B05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E12","notation":["51E12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized quadrangles and generalized polygons in finite geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E14","notation":["51E14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite partial geometries (general), nets, partial spreads"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E15","notation":["51E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite affine and projective planes (geometric aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E20","notation":["51E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial structures in finite projective spaces"},"scopeNote":{"en":["See also 05Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E21","notation":["51E21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Blocking sets, ovals, k-arcs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E22","notation":["51E22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear codes and caps in Galois spaces"},"scopeNote":{"en":["See also 94B05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E23","notation":["51E23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spreads and packing problems in finite geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E24","notation":["51E24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Buildings and the geometry of diagrams"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E25","notation":["51E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other finite nonlinear geometries"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E26","notation":["51E26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other finite linear geometries"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E30","notation":["51E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other finite incidence structures (geometric aspects)"},"scopeNote":{"en":["See also 05B30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51E99","notation":["51E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Exx","notation":["51Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51Fxx","notation":["51Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Metric geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51-XX","notation":["51-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51F05","notation":["51F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Absolute planes in metric geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Fxx","notation":["51Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51F10","notation":["51F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Absolute spaces in metric geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Fxx","notation":["51Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51F15","notation":["51F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Reflection groups, reflection geometries"},"scopeNote":{"en":["See also 20H10, 20H15; For Coxeter groups, see 20F55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Fxx","notation":["51Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51F20","notation":["51F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Congruence and orthogonality in metric geometry"},"scopeNote":{"en":["See also 20H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Fxx","notation":["51Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51F25","notation":["51F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orthogonal and unitary groups in metric geometry"},"scopeNote":{"en":["See also 20H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Fxx","notation":["51Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51F30","notation":["51F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lipschitz and coarse geometry of metric spaces"},"scopeNote":{"en":["See also 53C23"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Fxx","notation":["51Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51F99","notation":["51F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Fxx","notation":["51Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51Gxx","notation":["51Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered geometries (ordered incidence structures, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51-XX","notation":["51-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51G05","notation":["51G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ordered geometries (ordered incidence structures, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Gxx","notation":["51Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51G99","notation":["51G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Gxx","notation":["51Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51Hxx","notation":["51Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51-XX","notation":["51-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51H05","notation":["51H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of topological geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Hxx","notation":["51Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51H10","notation":["51H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological linear incidence structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Hxx","notation":["51Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51H15","notation":["51H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological nonlinear incidence structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Hxx","notation":["51Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51H20","notation":["51H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological geometries on manifolds"},"scopeNote":{"en":["See also 57-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Hxx","notation":["51Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51H25","notation":["51H25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometries with differentiable structure"},"scopeNote":{"en":["See also 53Cxx, especially 53C70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Hxx","notation":["51Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51H30","notation":["51H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometries with algebraic manifold structure"},"scopeNote":{"en":["See also 14-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Hxx","notation":["51Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51H99","notation":["51H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Hxx","notation":["51Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51Jxx","notation":["51Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Incidence groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51-XX","notation":["51-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51J05","notation":["51J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of incidence groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Jxx","notation":["51Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51J10","notation":["51J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Projective incidence groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Jxx","notation":["51Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51J15","notation":["51J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kinematic spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Jxx","notation":["51Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51J20","notation":["51J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Representation by near-fields and near-algebras"},"scopeNote":{"en":["See also 12K05, 16Y30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Jxx","notation":["51Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51J99","notation":["51J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Jxx","notation":["51Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51Kxx","notation":["51Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distance geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51-XX","notation":["51-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51K05","notation":["51K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of distance geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Kxx","notation":["51Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51K10","notation":["51K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Synthetic differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Kxx","notation":["51Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51K99","notation":["51K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Kxx","notation":["51Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51Lxx","notation":["51Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric order structures"},"scopeNote":{"en":["See also 53C75"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51-XX","notation":["51-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51L05","notation":["51L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometry of orders of nondifferentiable curves"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Lxx","notation":["51Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51L10","notation":["51L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Directly differentiable curves in geometric order structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Lxx","notation":["51Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51L15","notation":["51L15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"n-vertex theorems via direct methods"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Lxx","notation":["51Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51L20","notation":["51L20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometry of orders of surfaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Lxx","notation":["51Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51L99","notation":["51L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Lxx","notation":["51Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51Mxx","notation":["51Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real and complex geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51-XX","notation":["51-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51M04","notation":["51M04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elementary problems in Euclidean geometries"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Mxx","notation":["51Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51M05","notation":["51M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Euclidean geometries (general) and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Mxx","notation":["51Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51M09","notation":["51M09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elementary problems in hyperbolic and elliptic geometries"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Mxx","notation":["51Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51M10","notation":["51M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperbolic and elliptic geometries (general) and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Mxx","notation":["51Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51M15","notation":["51M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric constructions in real or complex geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Mxx","notation":["51Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51M16","notation":["51M16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inequalities and extremum problems in real or complex geometry"},"scopeNote":{"en":["For convex problems, see 52A40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Mxx","notation":["51Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51M20","notation":["51M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polyhedra and polytopes; regular figures, division of spaces"},"scopeNote":{"en":["See also 51F15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Mxx","notation":["51Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51M25","notation":["51M25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Length, area and volume in real or complex geometry"},"scopeNote":{"en":["See also 26B15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Mxx","notation":["51Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51M30","notation":["51M30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Line geometries and their generalizations"},"scopeNote":{"en":["See also 53A25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Mxx","notation":["51Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51M35","notation":["51M35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)"},"scopeNote":{"en":["See also 14M15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Mxx","notation":["51Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51M99","notation":["51M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Mxx","notation":["51Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51Nxx","notation":["51Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytic and descriptive geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51-XX","notation":["51-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51N05","notation":["51N05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Descriptive geometry"},"scopeNote":{"en":["See also 65D17, 68U07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Nxx","notation":["51Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51N10","notation":["51N10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Affine analytic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Nxx","notation":["51Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51N15","notation":["51N15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Projective analytic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Nxx","notation":["51Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51N20","notation":["51N20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Euclidean analytic geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Nxx","notation":["51Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51N25","notation":["51N25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytic geometry with other transformation groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Nxx","notation":["51Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51N30","notation":["51N30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometry of classical groups"},"scopeNote":{"en":["See also 14L35, 20Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Nxx","notation":["51Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51N35","notation":["51N35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Questions of classical algebraic geometry"},"scopeNote":{"en":["See also 14Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Nxx","notation":["51Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51N99","notation":["51N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Nxx","notation":["51Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51Pxx","notation":["51Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical or axiomatic geometry and physics (should also be assigned at least one other classification number from Sections 70–86)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51-XX","notation":["51-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51P05","notation":["51P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical or axiomatic geometry and physics (should also be assigned at least one other classification number from Sections 70–86)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Pxx","notation":["51Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/51P99","notation":["51P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/51Pxx","notation":["51Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52-XX","notation":["52-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convex and discrete geometry"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52-00","notation":["52-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to convex and discrete geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52-XX","notation":["52-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52-01","notation":["52-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52-XX","notation":["52-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52-02","notation":["52-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to convex and discrete geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52-XX","notation":["52-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52-03","notation":["52-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of convex and discrete geometry"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52-XX","notation":["52-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52-04","notation":["52-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to convex and discrete geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52-XX","notation":["52-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52-06","notation":["52-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to convex and discrete geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52-XX","notation":["52-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52-08","notation":["52-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to convex and discrete geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52-XX","notation":["52-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52-11","notation":["52-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to convex and discrete geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52-XX","notation":["52-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General convexity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52-XX","notation":["52-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A01","notation":["52A01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axiomatic and generalized convexity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A05","notation":["52A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convex sets without dimension restrictions (aspects of convex geometry)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A07","notation":["52A07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convex sets in topological vector spaces (aspects of convex geometry)"},"scopeNote":{"en":["See also 46A55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A10","notation":["52A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convex sets in 2 dimensions (including convex curves)"},"scopeNote":{"en":["See also 53A04"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A15","notation":["52A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convex sets in 3 dimensions (including convex surfaces)"},"scopeNote":{"en":["See also 53A05, 53C45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A20","notation":["52A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convex sets in n dimensions (including convex hypersurfaces)"},"scopeNote":{"en":["See also 53A07, 53C45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A21","notation":["52A21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry)"},"scopeNote":{"en":["See also 46Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A22","notation":["52A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random convex sets and integral geometry (aspects of convex geometry)"},"scopeNote":{"en":["See also 53C65, 60D05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A23","notation":["52A23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic theory of convex bodies"},"scopeNote":{"en":["See also 46B06"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A27","notation":["52A27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Approximation by convex sets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A30","notation":["52A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variants of convex sets (star-shaped, (m, n)-convex, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A35","notation":["52A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Helly-type theorems and geometric transversal theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A37","notation":["52A37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other problems of combinatorial convexity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A38","notation":["52A38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Length, area, volume and convex sets (aspects of convex geometry)"},"scopeNote":{"en":["See also 26B15, 28A75, 49Q20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A39","notation":["52A39"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mixed volumes and related topics in convex geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A40","notation":["52A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inequalities and extremum problems involving convexity in convex geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A41","notation":["52A41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convex functions and convex programs in convex geometry"},"scopeNote":{"en":["See also 26B25, 90C25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A55","notation":["52A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spherical and hyperbolic convexity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52A99","notation":["52A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Axx","notation":["52Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polytopes and polyhedra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52-XX","notation":["52-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52B05","notation":["52B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)"},"scopeNote":{"en":["See also 05Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52B10","notation":["52B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Three-dimensional polytopes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52B11","notation":["52B11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"n-dimensional polytopes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52B12","notation":["52B12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special polytopes (linear programming, centrally symmetric, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/52B20","notation":["52B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)"},"scopeNote":{"en":["See also 06A11, 13F20, 13F55, 13Hxx, 52C05, 52C07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52B22","notation":["52B22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Shellability for polytopes and polyhedra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52B35","notation":["52B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gale and other diagrams"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52B40","notation":["52B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)"},"scopeNote":{"en":["See also 05B35, 52Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52B45","notation":["52B45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dissections and valuations (Hilbert’s third problem, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52B55","notation":["52B55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational aspects related to convexity"},"scopeNote":{"en":["For computational methods, see 52-08; for computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx; See also 68Uxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52B60","notation":["52B60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Isoperimetric problems for polytopes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52B70","notation":["52B70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polyhedral manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52B99","notation":["52B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Bxx","notation":["52Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52Cxx","notation":["52Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discrete geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52-XX","notation":["52-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52C05","notation":["52C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattices and convex bodies in 2 dimensions (aspects of discrete geometry)"},"scopeNote":{"en":["See also 11H06, 11H31, 11P21"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Cxx","notation":["52Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52C07","notation":["52C07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattices and convex bodies in n dimensions (aspects of discrete geometry)"},"scopeNote":{"en":["See also 11H06, 11H31, 11P21"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Cxx","notation":["52Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52C10","notation":["52C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Erdős problems and related topics of discrete geometry"},"scopeNote":{"en":["See also 11Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Cxx","notation":["52Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52C15","notation":["52C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Packing and covering in 2 dimensions (aspects of discrete geometry)"},"scopeNote":{"en":["See also 05B40, 11H31"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Cxx","notation":["52Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52C17","notation":["52C17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Packing and covering in n dimensions (aspects of discrete geometry)"},"scopeNote":{"en":["See also 05B40, 11H31"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Cxx","notation":["52Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52C20","notation":["52C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Tilings in 2 dimensions (aspects of discrete geometry)"},"scopeNote":{"en":["See also 05B45, 51M20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Cxx","notation":["52Cxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/52C23","notation":["52C23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quasicrystals and aperiodic tilings in discrete geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Cxx","notation":["52Cxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/52C26","notation":["52C26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Circle packings and discrete conformal geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Cxx","notation":["52Cxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/52C40","notation":["52C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Oriented matroids in discrete geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Cxx","notation":["52Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52C45","notation":["52C45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial complexity of geometric structures"},"scopeNote":{"en":["See also 68U05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Cxx","notation":["52Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/52C99","notation":["52C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/52Cxx","notation":["52Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential geometry"},"scopeNote":{"en":["For differential topology, see 57Rxx; for foundational questions of differentiable manifolds, see 58Axx"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/53-01","notation":["53-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53-02","notation":["53-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53-03","notation":["53-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of differential geometry"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/53-06","notation":["53-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53-08","notation":["53-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53-11","notation":["53-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A04","notation":["53A04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Curves in Euclidean and related spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A05","notation":["53A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Surfaces in Euclidean and related spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A07","notation":["53A07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-dimensional and -codimensional surfaces in Euclidean and related n-spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A10","notation":["53A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Minimal surfaces in differential geometry, surfaces with prescribed mean curvature"},"scopeNote":{"en":["See also 49Q05, 49Q10, 53C42"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A15","notation":["53A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Affine differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A17","notation":["53A17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential geometric aspects in kinematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A20","notation":["53A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Projective differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A25","notation":["53A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential line geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/53A40","notation":["53A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other special differential geometries"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A45","notation":["53A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential geometric aspects in vector and tensor analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A55","notation":["53A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential invariants (local theory), geometric objects"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A60","notation":["53A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential geometry of webs"},"scopeNote":{"en":["See also 14C21, 20N05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A70","notation":["53A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discrete differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53A99","notation":["53A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Axx","notation":["53Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53B05","notation":["53B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear and affine connections"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53B10","notation":["53B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Projective connections"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53B12","notation":["53B12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential geometric aspects of statistical manifolds and information geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53B15","notation":["53B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other connections"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53B20","notation":["53B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local Riemannian geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53B21","notation":["53B21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methods of local Riemannian geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53B25","notation":["53B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local submanifolds"},"scopeNote":{"en":["See also 53C40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53B30","notation":["53B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local differential geometry of Lorentz metrics, indefinite metrics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53B35","notation":["53B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local differential geometry of Hermitian and Kählerian structures"},"scopeNote":{"en":["See also 32Qxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53B40","notation":["53B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local differential geometry of Finsler spaces and generalizations (areal metrics)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53B50","notation":["53B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of local differential geometry to the sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53B99","notation":["53B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Bxx","notation":["53Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global differential geometry  {For related bundle theory, see 55Rxx, 57Rxx]"},"scopeNote":{"en":["See also 51H25, 58-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C05","notation":["53C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connections, general theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C07","notation":["53C07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)"},"scopeNote":{"en":["See also 32Q20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C08","notation":["53C08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential geometric aspects of gerbes and differential characters"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C10","notation":["53C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"G-structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C12","notation":["53C12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foliations (differential geometric aspects)"},"scopeNote":{"en":["See also 57R30, 57R32"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C15","notation":["53C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General geometric structures on manifolds (almost complex, almost product structures, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C17","notation":["53C17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sub-Riemannian geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C18","notation":["53C18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Conformal structures on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C20","notation":["53C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global Riemannian geometry, including pinching"},"scopeNote":{"en":["See also 31C12, 58B20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C21","notation":["53C21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methods of global Riemannian geometry, including PDE methods; curvature restrictions"},"scopeNote":{"en":["See also 58J60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C22","notation":["53C22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geodesics in global differential geometry"},"scopeNote":{"en":["See also 58E10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C23","notation":["53C23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C24","notation":["53C24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rigidity results"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C25","notation":["53C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special Riemannian manifolds (Einstein, Sasakian, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C26","notation":["53C26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyper-Kähler and quaternionic Kähler geometry, “special” geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C27","notation":["53C27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spin and Spinc geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C28","notation":["53C28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Twistor methods in differential geometry"},"scopeNote":{"en":["See also 32L25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C29","notation":["53C29"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Issues of holonomy in differential geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C30","notation":["53C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential geometry of homogeneous manifolds"},"scopeNote":{"en":["See also 14M15, 14M17, 32M10, 57T15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C35","notation":["53C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential geometry of symmetric spaces"},"scopeNote":{"en":["See also 32M15, 57T15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C38","notation":["53C38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Calibrations and calibrated geometries"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C40","notation":["53C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global submanifolds"},"scopeNote":{"en":["See also 53B25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C42","notation":["53C42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)"},"scopeNote":{"en":["See also 49Q05, 49Q10, 53A10, 57R40, 57R42"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C43","notation":["53C43"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential geometric aspects of harmonic maps"},"scopeNote":{"en":["See also 58E20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C45","notation":["53C45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global surface theory (convex surfaces à la A. D. Aleksandrov)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C50","notation":["53C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C55","notation":["53C55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global differential geometry of Hermitian and Kählerian manifolds"},"scopeNote":{"en":["See also 32Qxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C56","notation":["53C56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other complex differential geometry"},"scopeNote":{"en":["See also 32Qxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C60","notation":["53C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global differential geometry of Finsler spaces and generalizations (areal metrics)"},"scopeNote":{"en":["See also 58B20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C65","notation":["53C65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integral geometry ; differential forms, currents, etc."},"scopeNote":{"en":["See also 52A22, 60D05; See mainly 58Axx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C70","notation":["53C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Direct methods (G-spaces of Busemann, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C75","notation":["53C75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric orders, order geometry"},"scopeNote":{"en":["See also 51Lxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C80","notation":["53C80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of global differential geometry to the sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53C99","notation":["53C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Cxx","notation":["53Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symplectic geometry, contact geometry"},"scopeNote":{"en":["See also 37Jxx, 70Gxx, 70Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D05","notation":["53D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symplectic manifolds, general"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D10","notation":["53D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Contact manifolds, general"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D12","notation":["53D12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lagrangian submanifolds; Maslov index"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D15","notation":["53D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Almost contact and almost symplectic manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D17","notation":["53D17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Poisson manifolds; Poisson groupoids and algebroids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D18","notation":["53D18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized geometries (à la Hitchin)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D20","notation":["53D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Momentum maps; symplectic reduction"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D22","notation":["53D22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Canonical transformations in symplectic and contact geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D25","notation":["53D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geodesic flows in symplectic geometry and contact geometry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D30","notation":["53D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symplectic structures of moduli spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D35","notation":["53D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global theory of symplectic and contact manifolds"},"scopeNote":{"en":["See also 57Rxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D37","notation":["53D37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category"},"scopeNote":{"en":["See also 14J33"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D40","notation":["53D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symplectic aspects of Floer homology and cohomology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D42","notation":["53D42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symplectic field theory; contact homology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D45","notation":["53D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gromov-Witten invariants, quantum cohomology, Frobenius manifolds"},"scopeNote":{"en":["See also 14N35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D50","notation":["53D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric quantization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D55","notation":["53D55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deformation quantization, star products"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53D99","notation":["53D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Dxx","notation":["53Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53Exx","notation":["53Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric evolution equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53E10","notation":["53E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Flows related to mean curvature"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Exx","notation":["53Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53E20","notation":["53E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ricci flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Exx","notation":["53Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53E30","notation":["53E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Exx","notation":["53Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53E40","notation":["53E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-order geometric flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Exx","notation":["53Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53E50","notation":["53E50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Flows related to symplectic and contact structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Exx","notation":["53Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53E99","notation":["53E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Exx","notation":["53Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53Zxx","notation":["53Zxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of differential geometry to sciences and engineering"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53-XX","notation":["53-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53Z05","notation":["53Z05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of differential geometry to physics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Zxx","notation":["53Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53Z10","notation":["53Z10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of differential geometry to biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Zxx","notation":["53Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53Z15","notation":["53Z15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of differential geometry to chemistry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Zxx","notation":["53Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53Z30","notation":["53Z30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of differential geometry to engineering"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Zxx","notation":["53Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53Z50","notation":["53Z50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of differential geometry to data and computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Zxx","notation":["53Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/53Z99","notation":["53Z99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/53Zxx","notation":["53Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General topology"},"scopeNote":{"en":["For the topology of manifolds of all dimensions, see 57Nxx"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54-00","notation":["54-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54-01","notation":["54-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54-02","notation":["54-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54-03","notation":["54-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of general topology"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54-04","notation":["54-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54-06","notation":["54-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54-08","notation":["54-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54-11","notation":["54-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54Axx","notation":["54Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalities in topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54A05","notation":["54A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological spaces and generalizations (closure spaces, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Axx","notation":["54Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54A10","notation":["54A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Axx","notation":["54Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54A15","notation":["54A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Syntopogeneous structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Axx","notation":["54Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54A20","notation":["54A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Axx","notation":["54Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54A25","notation":["54A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cardinality properties (cardinal functions and inequalities, discrete subsets)"},"scopeNote":{"en":["See also 03Exx; For ultrafilters, see 54D80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Axx","notation":["54Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54A35","notation":["54A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Consistency and independence results in general topology"},"scopeNote":{"en":["See also 03E35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Axx","notation":["54Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54A40","notation":["54A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy topology"},"scopeNote":{"en":["See also 03E72"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Axx","notation":["54Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54A99","notation":["54A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Axx","notation":["54Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54Bxx","notation":["54Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Basic constructions in general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54B05","notation":["54B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Subspaces in general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Bxx","notation":["54Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54B10","notation":["54B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Product spaces in general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Bxx","notation":["54Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54B15","notation":["54B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quotient spaces, decompositions in general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Bxx","notation":["54Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54B17","notation":["54B17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Adjunction spaces and similar constructions in general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Bxx","notation":["54Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54B20","notation":["54B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperspaces in general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Bxx","notation":["54Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54B30","notation":["54B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Categorical methods in general topology"},"scopeNote":{"en":["See also 18F60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Bxx","notation":["54Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54B35","notation":["54B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectra in general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Bxx","notation":["54Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54B40","notation":["54B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Presheaves and sheaves in general topology"},"scopeNote":{"en":["See also 18F20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Bxx","notation":["54Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54B99","notation":["54B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Bxx","notation":["54Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Maps and general types of topological spaces defined by maps"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C05","notation":["54C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuous maps"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C08","notation":["54C08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Weak and generalized continuity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C10","notation":["54C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special maps on topological spaces (open, closed, perfect, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C15","notation":["54C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Retraction"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C20","notation":["54C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extension of maps"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C25","notation":["54C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Embedding"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C30","notation":["54C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real-valued functions in general topology"},"scopeNote":{"en":["See also 26-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C35","notation":["54C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Function spaces in general topology"},"scopeNote":{"en":["See also 46Exx, 58D15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C40","notation":["54C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic properties of function spaces in general topology"},"scopeNote":{"en":["See also 46J10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C45","notation":["54C45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"C- and C ∗ -embedding"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C50","notation":["54C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topology of special sets defined by functions"},"scopeNote":{"en":["See also 26A21"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C55","notation":["54C55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)"},"scopeNote":{"en":["See also 55M15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C56","notation":["54C56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Shape theory in general topology"},"scopeNote":{"en":["See also 55P55, 57N25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C60","notation":["54C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set-valued maps in general topology"},"scopeNote":{"en":["See also 26E25, 28B20, 47H04, 58C06"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C65","notation":["54C65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Selections in general topology"},"scopeNote":{"en":["See also 28B20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C70","notation":["54C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Entropy in general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54C99","notation":["54C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Cxx","notation":["54Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fairly general properties of topological spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D05","notation":["54D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connected and locally connected spaces (general aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D10","notation":["54D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lower separation axioms (T0 –T3 , etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D15","notation":["54D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D20","notation":["54D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncompact covering properties (paracompact, Lindelöf, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D25","notation":["54D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"“P -minimal” and “P -closed” spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D30","notation":["54D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compactness"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D35","notation":["54D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extensions of spaces (compactifications, supercompactifications, completions, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D40","notation":["54D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Remainders in general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D45","notation":["54D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local compactness, σ-compactness"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D50","notation":["54D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"k-spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D55","notation":["54D55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sequential spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D60","notation":["54D60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Realcompactness and realcompactification"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D65","notation":["54D65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Separability of topological spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D70","notation":["54D70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Base properties of topological spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D80","notation":["54D80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special constructions of topological spaces (spaces of ultrafilters, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54D99","notation":["54D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Dxx","notation":["54Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological spaces with richer structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E05","notation":["54E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proximity structures and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E15","notation":["54E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Uniform structures and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E17","notation":["54E17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nearness spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E18","notation":["54E18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"p-spaces, M -spaces, σ-spaces, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E20","notation":["54E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stratifiable spaces, cosmic spaces, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E25","notation":["54E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semimetric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E30","notation":["54E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Moore spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E35","notation":["54E35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Metric spaces, metrizability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E40","notation":["54E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special maps on metric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E45","notation":["54E45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compact (locally compact) metric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E50","notation":["54E50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complete metric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E52","notation":["54E52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Baire category, Baire spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E55","notation":["54E55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bitopologies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E70","notation":["54E70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probabilistic metric spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54E99","notation":["54E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Exx","notation":["54Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54Fxx","notation":["54Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special properties of topological spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54F05","notation":["54F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces"},"scopeNote":{"en":["See also 06B30, 06F30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Fxx","notation":["54Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54F15","notation":["54F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continua and generalizations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Fxx","notation":["54Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54F16","notation":["54F16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperspaces of continua"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Fxx","notation":["54Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54F17","notation":["54F17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse limits of set-valued functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Fxx","notation":["54Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54F35","notation":["54F35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-dimensional local connectedness"},"scopeNote":{"en":["See also 55Mxx, 55Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Fxx","notation":["54Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54F45","notation":["54F45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dimension theory in general topology"},"scopeNote":{"en":["See also 55M10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Fxx","notation":["54Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54F50","notation":["54F50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological spaces of dimension ≤ 1; curves, dendrites"},"scopeNote":{"en":["See also 26A03"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Fxx","notation":["54Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54F55","notation":["54F55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unicoherence, multicoherence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Fxx","notation":["54Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54F65","notation":["54F65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological characterizations of particular spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Fxx","notation":["54Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54F99","notation":["54F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Fxx","notation":["54Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54Gxx","notation":["54Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Peculiar topological spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54G05","notation":["54G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extremally disconnected spaces, F -spaces, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Gxx","notation":["54Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54G10","notation":["54G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"P -spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Gxx","notation":["54Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54G12","notation":["54G12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Scattered spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Gxx","notation":["54Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54G15","notation":["54G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pathological topological spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Gxx","notation":["54Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54G20","notation":["54G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Counterexamples in general topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Gxx","notation":["54Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54G99","notation":["54G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Gxx","notation":["54Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54Hxx","notation":["54Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Connections of general topology with other structures, applications"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54H05","notation":["54H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)"},"scopeNote":{"en":["See also 03E15, 26A21, 28A05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Hxx","notation":["54Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54H10","notation":["54H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological representations of algebraic systems"},"scopeNote":{"en":["See also 22-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Hxx","notation":["54Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54H11","notation":["54H11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological groups (topological aspects)"},"scopeNote":{"en":["See also 22A05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Hxx","notation":["54Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54H12","notation":["54H12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological lattices, etc. (topological aspects)"},"scopeNote":{"en":["See also 06B30, 06F30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Hxx","notation":["54Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54H13","notation":["54H13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological fields, rings, etc. (topological aspects)"},"scopeNote":{"en":["See also 12Jxx; For algebraic aspects, see 13Jxx, 16W80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Hxx","notation":["54Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54H15","notation":["54H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transformation groups and semigroups (topological aspects)"},"scopeNote":{"en":["See also 20M20, 22-XX, 57Sxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Hxx","notation":["54Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54H25","notation":["54H25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fixed-point and coincidence theorems (topological aspects)"},"scopeNote":{"en":["See also 47H10, 55M20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Hxx","notation":["54Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54H30","notation":["54H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of general topology to computer science (e.g., digital topology, image processing)"},"scopeNote":{"en":["See also 68U03"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Hxx","notation":["54Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54H99","notation":["54H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Hxx","notation":["54Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54Jxx","notation":["54Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonstandard topology"},"scopeNote":{"en":["See also 03H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54-XX","notation":["54-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54J05","notation":["54J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonstandard topology"},"scopeNote":{"en":["See also 03H05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Jxx","notation":["54Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/54J99","notation":["54J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/54Jxx","notation":["54Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic topology"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55-00","notation":["55-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55-01","notation":["55-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55-02","notation":["55-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55-03","notation":["55-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of algebraic topology"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55-04","notation":["55-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55-06","notation":["55-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55-08","notation":["55-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55-11","notation":["55-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55Mxx","notation":["55Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical topics in algebraic topology"},"scopeNote":{"en":["For the topology of Euclidean spaces and manifolds, see 57Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55M05","notation":["55M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Duality in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Mxx","notation":["55Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55M10","notation":["55M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dimension theory in algebraic topology"},"scopeNote":{"en":["See also 54F45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Mxx","notation":["55Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55M15","notation":["55M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Absolute neighborhood retracts"},"scopeNote":{"en":["See also 54C55"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Mxx","notation":["55Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55M20","notation":["55M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fixed points and coincidences in algebraic topology"},"scopeNote":{"en":["See also 54H25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Mxx","notation":["55Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55M25","notation":["55M25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Degree, winding number"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Mxx","notation":["55Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55M30","notation":["55M30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Mxx","notation":["55Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55M35","notation":["55M35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite groups of transformations in algebraic topology (including Smith theory)"},"scopeNote":{"en":["See also 57S17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Mxx","notation":["55Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55M99","notation":["55M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Mxx","notation":["55Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homology and cohomology theories in algebraic topology"},"scopeNote":{"en":["See also 57Txx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N05","notation":["55N05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Čech types"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N07","notation":["55N07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Steenrod-Sitnikov homologies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N10","notation":["55N10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular homology and cohomology theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N15","notation":["55N15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological K-theory"},"scopeNote":{"en":["See also 19Lxx; For algebraic K-theory, see 18F25, 19-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N20","notation":["55N20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized (extraordinary) homology and cohomology theories in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N22","notation":["55N22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bordism and cobordism theories and formal group laws in algebraic topology"},"scopeNote":{"en":["See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N25","notation":["55N25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homology with local coefficients, equivariant cohomology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N30","notation":["55N30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sheaf cohomology in algebraic topology"},"scopeNote":{"en":["See also 18F20, 32C35, 32L10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N31","notation":["55N31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Persistent homology and applications, topological data analysis"},"scopeNote":{"en":["See also 62R40, 68T09"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N32","notation":["55N32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orbifold cohomology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N33","notation":["55N33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Intersection homology and cohomology in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N34","notation":["55N34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic cohomology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N35","notation":["55N35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other homology theories in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N40","notation":["55N40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axioms for homology theory and uniqueness theorems in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N45","notation":["55N45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Products and intersections in homology and cohomology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N91","notation":["55N91"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equivariant homology and cohomology in algebraic topology"},"scopeNote":{"en":["See also 19L47"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55N99","notation":["55N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Nxx","notation":["55Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homotopy theory"},"scopeNote":{"en":["For simple homotopy type, see 57Q10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P05","notation":["55P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homotopy extension properties, cofibrations in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P10","notation":["55P10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homotopy equivalences in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P15","notation":["55P15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classification of homotopy type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P20","notation":["55P20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Eilenberg-Mac Lane spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P25","notation":["55P25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spanier-Whitehead duality"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P30","notation":["55P30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Eckmann-Hilton duality"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P35","notation":["55P35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Loop spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P40","notation":["55P40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Suspensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P42","notation":["55P42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stable homotopy theory, spectra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P43","notation":["55P43"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectra with additional structure (E∞ , A∞ , ring spectra, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P45","notation":["55P45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"H-spaces and duals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P47","notation":["55P47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite loop spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P48","notation":["55P48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Loop space machines and operads in algebraic topology"},"scopeNote":{"en":["See also 18Mxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P50","notation":["55P50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"String topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P55","notation":["55P55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Shape theory"},"scopeNote":{"en":["See also 54C56, 55Q07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P57","notation":["55P57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proper homotopy theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P60","notation":["55P60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Localization and completion in homotopy theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P62","notation":["55P62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rational homotopy theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P65","notation":["55P65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homotopy functors in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P91","notation":["55P91"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equivariant homotopy theory in algebraic topology"},"scopeNote":{"en":["See also 19L47"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P92","notation":["55P92"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations between equivariant and nonequivariant homotopy theory in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55P99","notation":["55P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Pxx","notation":["55Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55Qxx","notation":["55Qxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homotopy groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55-XX","notation":["55-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/55Q07","notation":["55Q07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Shape groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Qxx","notation":["55Qxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/55Q51","notation":["55Q51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"vn -periodicity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Qxx","notation":["55Qxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/55R12","notation":["55R12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transfer for fiber spaces and bundles in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Rxx","notation":["55Rxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/55R55","notation":["55R55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fiberings with singularities in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Rxx","notation":["55Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55R60","notation":["55R60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Microbundles and block bundles in algebraic topology"},"scopeNote":{"en":["See also 57N55, 57Q50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Rxx","notation":["55Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55R65","notation":["55R65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of fiber spaces and bundles in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Rxx","notation":["55Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55R70","notation":["55R70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fibrewise topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Rxx","notation":["55Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55R80","notation":["55R80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discriminantal varieties and configuration spaces in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Rxx","notation":["55Rxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/55S05","notation":["55S05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Primary cohomology operations in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Sxx","notation":["55Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55S10","notation":["55S10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Steenrod algebra"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Sxx","notation":["55Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55S12","notation":["55S12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dyer-Lashof operations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Sxx","notation":["55Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55S15","notation":["55S15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symmetric products and cyclic products in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Sxx","notation":["55Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55S20","notation":["55S20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Secondary and higher cohomology operations in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Sxx","notation":["55Sxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/55S30","notation":["55S30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Massey products"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Sxx","notation":["55Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55S35","notation":["55S35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Obstruction theory in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Sxx","notation":["55Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55S36","notation":["55S36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extension and compression of mappings in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Sxx","notation":["55Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/55S37","notation":["55S37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classification of mappings in algebraic topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/55Sxx","notation":["55Sxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/57-01","notation":["57-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57-XX","notation":["57-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57-02","notation":["57-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57-XX","notation":["57-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57-03","notation":["57-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of manifolds and cell complexes"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57-XX","notation":["57-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/57R12","notation":["57R12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Smooth approximations in differential topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R15","notation":["57R15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R17","notation":["57R17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symplectic and contact topology in high or arbitrary dimension"},"scopeNote":{"en":["See also 57K33, 57K43"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R18","notation":["57R18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topology and geometry of orbifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R19","notation":["57R19"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic topology on manifolds and differential topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R20","notation":["57R20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Characteristic classes and numbers in differential topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R22","notation":["57R22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topology of vector bundles and fiber bundles"},"scopeNote":{"en":["See also 55Rxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R25","notation":["57R25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vector fields, frame fields in differential topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R27","notation":["57R27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Controllability of vector fields on C ∞ and real-analytic manifolds"},"scopeNote":{"en":["See also 49Qxx, 37C10, 93B05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R30","notation":["57R30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foliations in differential topology; geometric theory"},"scopeNote":{"en":["See also 53C12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R32","notation":["57R32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classifying spaces for foliations; Gelfand-Fuks cohomology"},"scopeNote":{"en":["See also 58H10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R35","notation":["57R35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differentiable mappings in differential topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R40","notation":["57R40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Embeddings in differential topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R42","notation":["57R42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Immersions in differential topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R45","notation":["57R45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singularities of differentiable mappings in differential topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R50","notation":["57R50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential topological aspects of diffeomorphisms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R52","notation":["57R52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Isotopy in differential topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R55","notation":["57R55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differentiable structures in differential topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R56","notation":["57R56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological quantum field theories (aspects of differential topology)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R57","notation":["57R57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of global analysis to structures on manifolds"},"scopeNote":{"en":["See also 57K41, 58-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R58","notation":["57R58"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Floer homology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R60","notation":["57R60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homotopy spheres, Poincaré conjecture"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R65","notation":["57R65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Surgery and handlebodies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R67","notation":["57R67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Surgery obstructions, Wall groups"},"scopeNote":{"en":["See also 19J25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R70","notation":["57R70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Critical points and critical submanifolds in differential topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R75","notation":["57R75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"O- and SO-cobordism"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R77","notation":["57R77"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex cobordism (U- and SU-cobordism)"},"scopeNote":{"en":["See also 55N22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R80","notation":["57R80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"h- and s-cobordism"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R85","notation":["57R85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equivariant cobordism"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R90","notation":["57R90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other types of cobordism"},"scopeNote":{"en":["See also 55N22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R91","notation":["57R91"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equivariant algebraic topology of manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R95","notation":["57R95"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Realizing cycles by submanifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57R99","notation":["57R99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Rxx","notation":["57Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57Sxx","notation":["57Sxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological transformation groups"},"scopeNote":{"en":["See also 20F34, 22-XX, 37-XX, 54H15, 58D05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57-XX","notation":["57-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57S05","notation":["57S05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological properties of groups of homeomorphisms or diffeomorphisms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Sxx","notation":["57Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57S10","notation":["57S10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compact groups of homeomorphisms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Sxx","notation":["57Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57S12","notation":["57S12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Toric topology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Sxx","notation":["57Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57S15","notation":["57S15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compact Lie groups of differentiable transformations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Sxx","notation":["57Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57S17","notation":["57S17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite transformation groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Sxx","notation":["57Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57S20","notation":["57S20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncompact Lie groups of transformations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Sxx","notation":["57Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57S25","notation":["57S25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groups acting on specific manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Sxx","notation":["57Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57S30","notation":["57S30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discontinuous groups of transformations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Sxx","notation":["57Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57S99","notation":["57S99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Sxx","notation":["57Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57Txx","notation":["57Txx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homology and homotopy of topological groups and related structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57-XX","notation":["57-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57T05","notation":["57T05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hopf algebras (aspects of homology and homotopy of topological groups)"},"scopeNote":{"en":["See also 16T05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Txx","notation":["57Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57T10","notation":["57T10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homology and cohomology of Lie groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Txx","notation":["57Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57T15","notation":["57T15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homology and cohomology of homogeneous spaces of Lie groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Txx","notation":["57Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57T20","notation":["57T20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homotopy groups of topological groups and homogeneous spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Txx","notation":["57Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57T25","notation":["57T25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homology and cohomology of H-spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Txx","notation":["57Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57T30","notation":["57T30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bar and cobar constructions"},"scopeNote":{"en":["See also 18N40, 55Uxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Txx","notation":["57Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57T35","notation":["57T35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of Eilenberg-Moore spectral sequences"},"scopeNote":{"en":["See also 55R20, 55T20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Txx","notation":["57Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57T99","notation":["57T99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Txx","notation":["57Txx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/57Z25","notation":["57Z25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations of manifolds and cell complexes with computer and data science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Zxx","notation":["57Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/57Z99","notation":["57Z99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/57Zxx","notation":["57Zxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/58-00","notation":["58-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to global analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58-01","notation":["58-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58-02","notation":["58-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to global analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58-03","notation":["58-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of global analysis"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58-04","notation":["58-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to global analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58-06","notation":["58-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to global analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58-08","notation":["58-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to global analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58-11","notation":["58-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to global analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of differentiable manifolds"},"scopeNote":{"en":["See also 32Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A03","notation":["58A03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topos-theoretic approach to differentiable manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A05","notation":["58A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differentiable manifolds, foundations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A07","notation":["58A07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real-analytic and Nash manifolds"},"scopeNote":{"en":["See also 14P20, 32C07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A10","notation":["58A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential forms in global analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A12","notation":["58A12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"de Rham theory in global analysis"},"scopeNote":{"en":["See also 14Fxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A14","notation":["58A14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hodge theory in global analysis"},"scopeNote":{"en":["See also 14C30, 14Fxx, 32J25, 32S35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A15","notation":["58A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exterior differential systems (Cartan theory)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A17","notation":["58A17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pfaffian systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A20","notation":["58A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jets in global analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A25","notation":["58A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Currents in global analysis"},"scopeNote":{"en":["See also 32C30, 53C65"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A30","notation":["58A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vector distributions (subbundles of the tangent bundles)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A32","notation":["58A32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Natural bundles"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A35","notation":["58A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stratified sets"},"scopeNote":{"en":["See also 32S60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A40","notation":["58A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A50","notation":["58A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Supermanifolds and graded manifolds"},"scopeNote":{"en":["See also 14A22, 32C11"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58A99","notation":["58A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Axx","notation":["58Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58Bxx","notation":["58Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite-dimensional manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58B05","notation":["58B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homotopy and topological questions for infinite-dimensional manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Bxx","notation":["58Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58B10","notation":["58B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differentiability questions for infinite-dimensional manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Bxx","notation":["58Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58B12","notation":["58B12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Questions of holomorphy and infinite-dimensional manifolds"},"scopeNote":{"en":["See also 32-XX, 46G20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Bxx","notation":["58Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58B15","notation":["58B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fredholm structures on infinite-dimensional manifolds"},"scopeNote":{"en":["See also 47A53"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Bxx","notation":["58Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58B20","notation":["58B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds"},"scopeNote":{"en":["See also 53C20, 53C60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Bxx","notation":["58Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58B25","notation":["58B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group structures and generalizations on infinite-dimensional manifolds"},"scopeNote":{"en":["See also 22E65, 58D05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Bxx","notation":["58Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58B32","notation":["58B32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometry of quantum groups"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Bxx","notation":["58Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58B34","notation":["58B34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative geometry (à la Connes)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Bxx","notation":["58Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58B99","notation":["58B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Bxx","notation":["58Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Calculus on manifolds; nonlinear operators"},"scopeNote":{"en":["See also 46Txx, 47Hxx, 47Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58C05","notation":["58C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real-valued functions on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58C06","notation":["58C06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Set-valued and function-space-valued mappings on manifolds"},"scopeNote":{"en":["See also 47H04, 54C60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58C07","notation":["58C07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuity properties of mappings on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58C10","notation":["58C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Holomorphic maps on manifolds"},"scopeNote":{"en":["See also 32-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58C15","notation":["58C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Implicit function theorems; global Newton methods on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58C20","notation":["58C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differentiation theory (Gateaux, Fréchet, etc.) on manifolds"},"scopeNote":{"en":["See also 26Exx, 46G05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58C25","notation":["58C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differentiable maps on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58C30","notation":["58C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fixed-point theorems on manifolds"},"scopeNote":{"en":["See also 47H10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58C35","notation":["58C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integration on manifolds; measures on manifolds"},"scopeNote":{"en":["See also 28Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58C40","notation":["58C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral theory; eigenvalue problems on manifolds"},"scopeNote":{"en":["See also 47J10, 58E07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58C50","notation":["58C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis on supermanifolds or graded manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58C99","notation":["58C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Cxx","notation":["58Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces and manifolds of mappings (including nonlinear versions of 46Exx)"},"scopeNote":{"en":["See also 46Txx, 53Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58D05","notation":["58D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groups of diffeomorphisms and homeomorphisms as manifolds"},"scopeNote":{"en":["See also 22E65, 57S05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58D07","notation":["58D07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groups and semigroups of nonlinear operators"},"scopeNote":{"en":["See also 17B65, 47H20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58D10","notation":["58D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces of embeddings and immersions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58D15","notation":["58D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Manifolds of mappings"},"scopeNote":{"en":["See also 46T10, 54C35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58D17","notation":["58D17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Manifolds of metrics (especially Riemannian)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58D19","notation":["58D19"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group actions and symmetry properties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58D20","notation":["58D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measures (Gaussian, cylindrical, etc.) on manifolds of maps"},"scopeNote":{"en":["See also 28Cxx, 46T12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58D25","notation":["58D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equations in function spaces; evolution equations"},"scopeNote":{"en":["See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58D27","notation":["58D27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Moduli problems for differential geometric structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58D29","notation":["58D29"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Moduli problems for topological structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58D30","notation":["58D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of manifolds of mappings to the sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58D99","notation":["58D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Dxx","notation":["58Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational problems in infinite-dimensional spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E05","notation":["58E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E07","notation":["58E07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational problems in abstract bifurcation theory in infinite-dimensional spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E09","notation":["58E09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group-invariant bifurcation theory in infinite-dimensional spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E10","notation":["58E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational problems in applications to the theory of geodesics (problems in one independent variable)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E11","notation":["58E11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Critical metrics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E12","notation":["58E12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational problems concerning minimal surfaces (problems in two independent variables)"},"scopeNote":{"en":["See also 49Q05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E15","notation":["58E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational problems concerning extremal problems in several variables; Yang-Mills functionals , etc."},"scopeNote":{"en":["See also 81T13"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E17","notation":["58E17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiobjective variational problems, Pareto optimality, applications to economics, etc."},"scopeNote":{"en":["See also 90C29, 91Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E20","notation":["58E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Harmonic maps, etc."},"scopeNote":{"en":["See also 53C43"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E25","notation":["58E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of variational problems to control theory"},"scopeNote":{"en":["See also 49-XX, 93-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E30","notation":["58E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational principles in infinite-dimensional spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E35","notation":["58E35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational inequalities (global problems) in infinite-dimensional spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E40","notation":["58E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational aspects of group actions in infinite-dimensional spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E50","notation":["58E50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of variational problems in infinite-dimensional spaces to the sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58E99","notation":["58E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Exx","notation":["58Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58Hxx","notation":["58Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pseudogroups, differentiable groupoids and general structures on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58H05","notation":["58H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pseudogroups and differentiable groupoids"},"scopeNote":{"en":["See also 22A22, 22E65"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Hxx","notation":["58Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58H10","notation":["58H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)"},"scopeNote":{"en":["See also 57R32"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Hxx","notation":["58Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58H15","notation":["58H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deformations of general structures on manifolds"},"scopeNote":{"en":["See also 32Gxx, 58J10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Hxx","notation":["58Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58H99","notation":["58H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Hxx","notation":["58Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Partial differential equations on manifolds; differential operators"},"scopeNote":{"en":["See also 32Wxx, 35-XX, 53Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J05","notation":["58J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic equations on manifolds, general theory"},"scopeNote":{"en":["See also 35-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J10","notation":["58J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential complexes ; elliptic complexes"},"scopeNote":{"en":["See also 35Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J15","notation":["58J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations of PDEs on manifolds with hyperfunctions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J20","notation":["58J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Index theory and related fixed-point theorems on manifolds"},"scopeNote":{"en":["See also 19K56, 46L80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J22","notation":["58J22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exotic index theories on manifolds"},"scopeNote":{"en":["See also 19K56, 46L05, 46L10, 46L80, 46M20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J26","notation":["58J26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Elliptic genera"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J28","notation":["58J28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Eta-invariants, Chern-Simons invariants"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J30","notation":["58J30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J32","notation":["58J32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary value problems on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J35","notation":["58J35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Heat and other parabolic equation methods for PDEs on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J37","notation":["58J37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perturbations of PDEs on manifolds; asymptotics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J40","notation":["58J40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pseudodifferential and Fourier integral operators on manifolds"},"scopeNote":{"en":["See also 35Sxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J42","notation":["58J42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative global analysis, noncommutative residues"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J45","notation":["58J45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hyperbolic equations on manifolds"},"scopeNote":{"en":["See also 35Lxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J47","notation":["58J47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Propagation of singularities; initial value problems on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J50","notation":["58J50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral problems; spectral geometry; scattering theory on manifolds"},"scopeNote":{"en":["See also 35Pxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J51","notation":["58J51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J52","notation":["58J52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Determinants and determinant bundles, analytic torsion"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J53","notation":["58J53"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Isospectrality"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J55","notation":["58J55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcation theory for PDEs on manifolds"},"scopeNote":{"en":["See also 35B32"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J60","notation":["58J60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J65","notation":["58J65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Diffusion processes and stochastic analysis on manifolds"},"scopeNote":{"en":["See also 35R60, 60H10, 60J60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J70","notation":["58J70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Invariance and symmetry properties for PDEs on manifolds"},"scopeNote":{"en":["See also 35A30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J72","notation":["58J72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds"},"scopeNote":{"en":["See also 35A22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J90","notation":["58J90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of PDEs on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58J99","notation":["58J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Jxx","notation":["58Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of singularities and catastrophe theory"},"scopeNote":{"en":["See also 32Sxx, 37-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K05","notation":["58K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Critical points of functions and mappings on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K10","notation":["58K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monodromy on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K15","notation":["58K15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological properties of mappings on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K20","notation":["58K20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic and analytic properties of mappings on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K25","notation":["58K25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability theory for manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K30","notation":["58K30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Global theory of singularities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K35","notation":["58K35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Catastrophe theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K40","notation":["58K40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classification; finite determinacy of map germs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K45","notation":["58K45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singularities of vector fields, topological aspects"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K50","notation":["58K50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Normal forms on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K55","notation":["58K55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic behavior of solutions to equations on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K60","notation":["58K60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deformation of singularities"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K65","notation":["58K65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological invariants on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K70","notation":["58K70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symmetries, equivariance on manifolds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58K99","notation":["58K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Kxx","notation":["58Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58Zxx","notation":["58Zxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of global analysis to the sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58-XX","notation":["58-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58Z05","notation":["58Z05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of global analysis to the sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Zxx","notation":["58Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/58Z99","notation":["58Z99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/58Zxx","notation":["58Zxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probability theory and stochastic processes"},"scopeNote":{"en":["For additional applications, see 05Cxx, 11Kxx, 34-XX, 35-XX, 62-XX, 90-XX, 76-XX, 81-XX, 82-XX, 91-XX, 92-XX, 93-XX, 94-XX"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60-00","notation":["60-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to probability theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60-01","notation":["60-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60-02","notation":["60-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to probability theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60-03","notation":["60-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of probability theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60-04","notation":["60-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to probability theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60-06","notation":["60-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to probability theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60-08","notation":["60-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to probability theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60-11","notation":["60-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to probability theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60Axx","notation":["60Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations of probability theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60A05","notation":["60A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axioms; other general questions in probability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Axx","notation":["60Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60A10","notation":["60A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probabilistic measure theory"},"scopeNote":{"en":["For ergodic theory, see 28Dxx, 60Fxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Axx","notation":["60Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60A86","notation":["60A86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy probability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Axx","notation":["60Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60A99","notation":["60A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Axx","notation":["60Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60Bxx","notation":["60Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probability theory on algebraic and topological structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60B05","notation":["60B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probability measures on topological spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Bxx","notation":["60Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60B10","notation":["60B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convergence of probability measures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Bxx","notation":["60Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60B11","notation":["60B11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probability theory on linear topological spaces"},"scopeNote":{"en":["See also 28C20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Bxx","notation":["60Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60B12","notation":["60B12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Limit theorems for vector-valued random variables (infinite-dimensional case)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Bxx","notation":["60Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60B15","notation":["60B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probability measures on groups or semigroups, Fourier transforms, factorization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Bxx","notation":["60Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60B20","notation":["60B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random matrices (probabilistic aspects)"},"scopeNote":{"en":["For algebraic aspects, see 15B52"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Bxx","notation":["60Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60B99","notation":["60B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Bxx","notation":["60Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60Cxx","notation":["60Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial probability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60C05","notation":["60C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial probability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Cxx","notation":["60Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60C99","notation":["60C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Cxx","notation":["60Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60Dxx","notation":["60Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric probability and stochastic geometry"},"scopeNote":{"en":["See also 52A22, 53C65"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60D05","notation":["60D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric probability and stochastic geometry"},"scopeNote":{"en":["See also 52A22, 53C65"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Dxx","notation":["60Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60D99","notation":["60D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Dxx","notation":["60Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60Exx","notation":["60Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distribution theory"},"scopeNote":{"en":["See also 62Exx, 62Hxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60E05","notation":["60E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probability distributions: general theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Exx","notation":["60Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60E07","notation":["60E07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinitely divisible distributions; stable distributions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Exx","notation":["60Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60E10","notation":["60E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Characteristic functions; other transforms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Exx","notation":["60Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60E15","notation":["60E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inequalities; stochastic orderings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Exx","notation":["60Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60E99","notation":["60E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Exx","notation":["60Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60Fxx","notation":["60Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Limit theorems in probability theory"},"scopeNote":{"en":["See also 28Dxx, 60B12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60F05","notation":["60F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Central limit and other weak theorems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Fxx","notation":["60Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60F10","notation":["60F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Large deviations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Fxx","notation":["60Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60F15","notation":["60F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Strong limit theorems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Fxx","notation":["60Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60F17","notation":["60F17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional limit theorems; invariance principles"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Fxx","notation":["60Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60F20","notation":["60F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Zero-one laws"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Fxx","notation":["60Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60F25","notation":["60F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lp -limit theorems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Fxx","notation":["60Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60F99","notation":["60F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Fxx","notation":["60Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G05","notation":["60G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations of stochastic processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G07","notation":["60G07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of stochastic processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G09","notation":["60G09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exchangeability for stochastic processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G10","notation":["60G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stationary stochastic processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G12","notation":["60G12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General second-order stochastic processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G15","notation":["60G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gaussian processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G17","notation":["60G17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sample path properties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G18","notation":["60G18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Self-similar stochastic processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G20","notation":["60G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized stochastic processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G22","notation":["60G22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fractional processes, including fractional Brownian motion"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G25","notation":["60G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Prediction theory (aspects of stochastic processes)"},"scopeNote":{"en":["See also 62M20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G30","notation":["60G30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuity and singularity of induced measures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G35","notation":["60G35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Signal detection and filtering (aspects of stochastic processes)"},"scopeNote":{"en":["See also 62M20, 93E10, 93E11, 94Axx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G40","notation":["60G40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stopping times; optimal stopping problems; gambling theory"},"scopeNote":{"en":["See also 62L15, 91A60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G42","notation":["60G42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Martingales with discrete parameter"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G44","notation":["60G44"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Martingales with continuous parameter"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G46","notation":["60G46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Martingales and classical analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G48","notation":["60G48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalizations of martingales"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G50","notation":["60G50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sums of independent random variables; random walks"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G51","notation":["60G51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Processes with independent increments; Lévy processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G52","notation":["60G52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stable stochastic processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G53","notation":["60G53"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Feller processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G55","notation":["60G55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Point processes (e.g., Poisson, Cox, Hawkes processes)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G57","notation":["60G57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random measures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G60","notation":["60G60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random fields"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G65","notation":["60G65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear processes (e.g., G-Brownian motion, G-Lévy processes)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G70","notation":["60G70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extreme value theory; extremal stochastic processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60G99","notation":["60G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Gxx","notation":["60Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic analysis"},"scopeNote":{"en":["See also 58J65"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60H05","notation":["60H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic integrals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60H07","notation":["60H07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic calculus of variations and the Malliavin calculus"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60H10","notation":["60H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic ordinary differential equations (aspects of stochastic analysis)"},"scopeNote":{"en":["See also 34F05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60H15","notation":["60H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic partial differential equations (aspects of stochastic analysis)"},"scopeNote":{"en":["See also 35R60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60H17","notation":["60H17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singular stochastic partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60H20","notation":["60H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic integral equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60H25","notation":["60H25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random operators and equations (aspects of stochastic analysis)"},"scopeNote":{"en":["See also 47B80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60H30","notation":["60H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of stochastic analysis (to PDEs, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60H35","notation":["60H35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for stochastic equations (aspects of stochastic analysis)"},"scopeNote":{"en":["See also 65C30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60H40","notation":["60H40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"White noise theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60H50","notation":["60H50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Regularization by noise"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60H99","notation":["60H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Hxx","notation":["60Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Markov processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J05","notation":["60J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discrete-time Markov processes on general state spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J10","notation":["60J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Markov chains (discrete-time Markov processes on discrete state spaces)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J20","notation":["60J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)"},"scopeNote":{"en":["See also 90B30, 91D10, 91E40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J22","notation":["60J22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods in Markov chains"},"scopeNote":{"en":["See also 65C40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J25","notation":["60J25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuous-time Markov processes on general state spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J27","notation":["60J27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuous-time Markov processes on discrete state spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J28","notation":["60J28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of continuous-time Markov processes on discrete state spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J35","notation":["60J35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transition functions, generators and resolvents"},"scopeNote":{"en":["See also 47D03, 47D07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J40","notation":["60J40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Right processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J45","notation":["60J45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probabilistic potential theory"},"scopeNote":{"en":["See also 31Cxx, 31D05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J46","notation":["60J46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dirichlet form methods in Markov processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J50","notation":["60J50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary theory for Markov processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J55","notation":["60J55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Local time and additive functionals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J57","notation":["60J57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiplicative functionals and Markov processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J60","notation":["60J60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Diffusion processes"},"scopeNote":{"en":["See also 58J65"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J65","notation":["60J65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Brownian motion"},"scopeNote":{"en":["See also 58J65"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J67","notation":["60J67"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic (Schramm-)Loewner evolution (SLE)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J68","notation":["60J68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Superprocesses"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J70","notation":["60J70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)"},"scopeNote":{"en":["See also 92Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J75","notation":["60J75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jump processes on discrete state spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J76","notation":["60J76"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jump processes on general state spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J80","notation":["60J80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Branching processes (Galton-Watson, birth-and-death, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J85","notation":["60J85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of branching processes"},"scopeNote":{"en":["See also 92Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J90","notation":["60J90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Coalescent processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J95","notation":["60J95"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of coalescent processes"},"scopeNote":{"en":["See also 92Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60J99","notation":["60J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Jxx","notation":["60Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60Kxx","notation":["60Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60K05","notation":["60K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Renewal theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Kxx","notation":["60Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60K10","notation":["60K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of renewal theory (reliability, demand theory, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Kxx","notation":["60Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60K15","notation":["60K15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Markov renewal processes, semi-Markov processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Kxx","notation":["60Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60K20","notation":["60K20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of Markov renewal processes (reliability, queueing networks, etc.)"},"scopeNote":{"en":["See also 90Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Kxx","notation":["60Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60K25","notation":["60K25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Queueing theory (aspects of probability theory)"},"scopeNote":{"en":["See also 68M20, 90B22"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Kxx","notation":["60Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60K30","notation":["60K30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of queueing theory (congestion, allocation, storage, traffic, etc.)"},"scopeNote":{"en":["See also 90Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Kxx","notation":["60Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60K35","notation":["60K35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Interacting random processes; statistical mechanics type models; percolation theory"},"scopeNote":{"en":["See also 82B43, 82C43"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Kxx","notation":["60Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60K37","notation":["60K37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Processes in random environments"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Kxx","notation":["60Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60K40","notation":["60K40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other physical applications of random processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Kxx","notation":["60Kxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/60Lxx","notation":["60Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rough analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60-XX","notation":["60-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60L10","notation":["60L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Signatures and data streams"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Lxx","notation":["60Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60L20","notation":["60L20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rough paths"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Lxx","notation":["60Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60L30","notation":["60L30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Regularity structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Lxx","notation":["60Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60L40","notation":["60L40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Paracontrolled distributions and alternative approaches"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Lxx","notation":["60Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60L50","notation":["60L50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rough partial differential equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Lxx","notation":["60Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60L70","notation":["60L70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic structures and computation"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Lxx","notation":["60Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/60L90","notation":["60L90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of rough analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/60Lxx","notation":["60Lxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/62-02","notation":["62-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to statistics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62-XX","notation":["62-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/62-03","notation":["62-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of statistics"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62-XX","notation":["62-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/62-04","notation":["62-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to statistics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62-XX","notation":["62-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/62A01","notation":["62A01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations and philosophical topics in statistics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62Axx","notation":["62Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/62A86","notation":["62A86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy analysis in statistics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62Axx","notation":["62Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/62B11","notation":["62B11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Information geometry (statistical aspects)"},"scopeNote":{"en":["For differential geometric aspects, see 53B12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62Bxx","notation":["62Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/62B15","notation":["62B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of statistical experiments"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62Bxx","notation":["62Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/62B86","notation":["62B86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical aspects of fuzziness, sufficiency, and information"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62Bxx","notation":["62Bxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/62C05","notation":["62C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General considerations in statistical decision theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62Cxx","notation":["62Cxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/62C10","notation":["62C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bayesian problems; characterization of Bayes procedures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62Cxx","notation":["62Cxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/62C20","notation":["62C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Minimax procedures in statistical decision theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62Cxx","notation":["62Cxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/62Dxx","notation":["62Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical sampling theory, sample surveys"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62-XX","notation":["62-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/62D10","notation":["62D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Missing data"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62Dxx","notation":["62Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/62D20","notation":["62D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Causal inference from observational studies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62Dxx","notation":["62Dxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/62N03","notation":["62N03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Testing in survival analysis and censored data"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62Nxx","notation":["62Nxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/62N86","notation":["62N86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzziness, and survival analysis and censored data"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/62Nxx","notation":["62Nxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/65D17","notation":["65D17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computer-aided design (modeling of curves and surfaces)"},"scopeNote":{"en":["See also 68U07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/65Dxx","notation":["65Dxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/65D19","notation":["65D19"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational issues in computer and robotic vision"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/65Dxx","notation":["65Dxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computer science"},"scopeNote":{"en":["For papers containing software, source code, etc. in a specific mathematical area, see the classification number -04 in that area"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68-00","notation":["68-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68-01","notation":["68-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68-02","notation":["68-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68-03","notation":["68-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of computer science"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68-04","notation":["68-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68-06","notation":["68-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68-11","notation":["68-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Mxx","notation":["68Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computer system organization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68M01","notation":["68M01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General theory of computer systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Mxx","notation":["68Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68M07","notation":["68M07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical problems of computer architecture"},"scopeNote":{"en":["See also 68W35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Mxx","notation":["68Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68M10","notation":["68M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Network design and communication in computer systems"},"scopeNote":{"en":["See also 68R10, 90B18"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Mxx","notation":["68Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68M11","notation":["68M11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Internet topics"},"scopeNote":{"en":["See also 68U35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Mxx","notation":["68Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68M12","notation":["68M12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Network protocols"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Mxx","notation":["68Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68M14","notation":["68M14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distributed systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Mxx","notation":["68Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68M15","notation":["68M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Reliability, testing and fault tolerance of networks and computer systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Mxx","notation":["68Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68M18","notation":["68M18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Wireless sensor networks as related to computer science"},"scopeNote":{"en":["See also 90B18, 90B80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Mxx","notation":["68Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68M20","notation":["68M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Performance evaluation, queueing, and scheduling in the context of computer systems"},"scopeNote":{"en":["See also 60K20, 60K25, 90B22, 90B35, 90B36"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Mxx","notation":["68Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68M25","notation":["68M25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computer security"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Mxx","notation":["68Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68M99","notation":["68M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Mxx","notation":["68Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Nxx","notation":["68Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of software"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68N01","notation":["68N01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General topics in the theory of software"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Nxx","notation":["68Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68N15","notation":["68N15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of programming languages"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Nxx","notation":["68Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68N17","notation":["68N17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logic programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Nxx","notation":["68Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68N18","notation":["68N18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional programming and lambda calculus"},"scopeNote":{"en":["See also 03B40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Nxx","notation":["68Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68N19","notation":["68N19"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Nxx","notation":["68Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68N20","notation":["68N20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of compilers and interpreters"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Nxx","notation":["68Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68N25","notation":["68N25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of operating systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Nxx","notation":["68Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68N30","notation":["68N30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Nxx","notation":["68Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68N99","notation":["68N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Nxx","notation":["68Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Pxx","notation":["68Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of data"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68P01","notation":["68P01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General topics in the theory of data"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Pxx","notation":["68Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68P05","notation":["68P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Data structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Pxx","notation":["68Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68P10","notation":["68P10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Searching and sorting"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Pxx","notation":["68Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68P15","notation":["68P15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Database theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Pxx","notation":["68Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68P20","notation":["68P20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Information storage and retrieval of data"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Pxx","notation":["68Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68P25","notation":["68P25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Data encryption (aspects in computer science)"},"scopeNote":{"en":["See also 81P94, 94A60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Pxx","notation":["68Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68P27","notation":["68P27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Privacy of data"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Pxx","notation":["68Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68P30","notation":["68P30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science)"},"scopeNote":{"en":["See also 94Axx, 94Bxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Pxx","notation":["68Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68P99","notation":["68P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Pxx","notation":["68Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of computing"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q01","notation":["68Q01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General topics in the theory of computing"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q04","notation":["68Q04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical models of computation (Turing machines, etc.)"},"scopeNote":{"en":["See also 03D10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q06","notation":["68Q06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Networks and circuits as models of computation; circuit complexity"},"scopeNote":{"en":["See also 94C11"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q07","notation":["68Q07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biologically inspired models of computation (DNA computing, membrane computing, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q09","notation":["68Q09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other nonclassical models of computation"},"scopeNote":{"en":["For quantum computing, see mainly 68Q12, 81P68"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q10","notation":["68Q10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)"},"scopeNote":{"en":["See also 68Q85"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q11","notation":["68Q11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Communication complexity, information complexity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q12","notation":["68Q12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum algorithms and complexity in the theory of computing"},"scopeNote":{"en":["See also 68Q09, 81P68"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q15","notation":["68Q15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complexity classes (hierarchies, relations among complexity classes, etc.)"},"scopeNote":{"en":["See also 03D15, 68Q17, 68Q19"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q17","notation":["68Q17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)"},"scopeNote":{"en":["See also 68Q15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q19","notation":["68Q19"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Descriptive complexity and finite models"},"scopeNote":{"en":["See also 03C13"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q25","notation":["68Q25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis of algorithms and problem complexity"},"scopeNote":{"en":["See also 68W40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q27","notation":["68Q27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Parameterized complexity, tractability and kernelization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q30","notation":["68Q30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algorithmic information theory (Kolmogorov complexity, etc.)"},"scopeNote":{"en":["See also 03D32"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q32","notation":["68Q32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational learning theory"},"scopeNote":{"en":["See also 68T05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q42","notation":["68Q42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Grammars and rewriting systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q45","notation":["68Q45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Formal languages and automata"},"scopeNote":{"en":["See also 03D05, 68Q70, 94A45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q55","notation":["68Q55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semantics in the theory of computing"},"scopeNote":{"en":["See also 03B70, 06B35, 18C50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q60","notation":["68Q60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Specification and verification (program logics, model checking, etc.)"},"scopeNote":{"en":["See also 03B70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q65","notation":["68Q65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract data types; algebraic specification"},"scopeNote":{"en":["See also 18C50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q70","notation":["68Q70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic theory of languages and automata"},"scopeNote":{"en":["See also 18B20, 20M35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q80","notation":["68Q80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cellular automata (computational aspects)"},"scopeNote":{"en":["For cellular automata as dynamical systems, see 37B15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q85","notation":["68Q85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q87","notation":["68Q87"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)"},"scopeNote":{"en":["See also 68W20, 68W40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Q99","notation":["68Q99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Qxx","notation":["68Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Rxx","notation":["68Rxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discrete mathematics in relation to computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68R01","notation":["68R01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General topics of discrete mathematics in relation to computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Rxx","notation":["68Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68R05","notation":["68R05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorics in computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Rxx","notation":["68Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68R07","notation":["68R07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational aspects of satisfiability"},"scopeNote":{"en":["See also 68T20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Rxx","notation":["68Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68R10","notation":["68R10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Graph theory (including graph drawing) in computer science"},"scopeNote":{"en":["See also 05Cxx, 90B10, 90C35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Rxx","notation":["68Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68R12","notation":["68R12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Metric embeddings as related to computational problems and algorithms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Rxx","notation":["68Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68R15","notation":["68R15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorics on words"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Rxx","notation":["68Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68R99","notation":["68R99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Rxx","notation":["68Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Artificial intelligence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T01","notation":["68T01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General topics in artificial intelligence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T05","notation":["68T05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Learning and adaptive systems in artificial intelligence"},"scopeNote":{"en":["See also 68Q32"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T07","notation":["68T07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Artificial neural networks and deep learning"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T09","notation":["68T09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational aspects of data analysis and big data"},"scopeNote":{"en":["See also 62R07; For homological aspects, see 55N31"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T10","notation":["68T10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pattern recognition, speech recognition"},"scopeNote":{"en":["For cluster analysis, see 62H30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T20","notation":["68T20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T27","notation":["68T27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logic in artificial intelligence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T30","notation":["68T30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Knowledge representation"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T35","notation":["68T35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T37","notation":["68T37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Reasoning under uncertainty in the context of artificial intelligence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T40","notation":["68T40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Artificial intelligence for robotics"},"scopeNote":{"en":["See also 93C85"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T42","notation":["68T42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Agent technology and artificial intelligence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T45","notation":["68T45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Machine vision and scene understanding"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T50","notation":["68T50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Natural language processing"},"scopeNote":{"en":["See also 03B65, 91F20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68T99","notation":["68T99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Txx","notation":["68Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Uxx","notation":["68Uxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computing methodologies and applications"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68U01","notation":["68U01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General topics in computing methodologies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Uxx","notation":["68Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68U03","notation":["68U03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational aspects of digital topology"},"scopeNote":{"en":["For topological aspects, see 54H30; for homological aspects, see 55-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Uxx","notation":["68Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68U05","notation":["68U05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computer graphics; computational geometry (digital and algorithmic aspects)"},"scopeNote":{"en":["For methods of numerical mathematics, see 65D18"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Uxx","notation":["68Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68U07","notation":["68U07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computer science aspects of computer-aided design"},"scopeNote":{"en":["For methods of numerical mathematics, see 65D17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Uxx","notation":["68Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68U10","notation":["68U10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computing methodologies for image processing"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Uxx","notation":["68Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68U15","notation":["68U15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computing methodologies for text processing; mathematical typography"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Uxx","notation":["68Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68U35","notation":["68U35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.)"},"scopeNote":{"en":["See also 68M11"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Uxx","notation":["68Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68U99","notation":["68U99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Uxx","notation":["68Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Vxx","notation":["68Vxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computer science support for mathematical research and practice"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68V05","notation":["68V05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computer assisted proofs of proofs-by-exhaustion type"},"scopeNote":{"en":["For rigorous numerics, see 65Gxx; for proofs employing automated or interactive theorem provers, see 68V15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Vxx","notation":["68Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68V15","notation":["68V15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.)"},"scopeNote":{"en":["See also 03B35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Vxx","notation":["68Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68V20","notation":["68V20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Formalization of mathematics in connection with theorem provers"},"scopeNote":{"en":["See also 03B35, 68V15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Vxx","notation":["68Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68V25","notation":["68V25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Presentation and content markup for mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Vxx","notation":["68Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68V30","notation":["68V30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical knowledge management"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Vxx","notation":["68Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68V35","notation":["68V35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Digital mathematics libraries and repositories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Vxx","notation":["68Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68V99","notation":["68V99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Vxx","notation":["68Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algorithms in computer science"},"scopeNote":{"en":["For numerical algorithms, see 65-XX; for combinatorics and graph theory, see 05C85, 68Rxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68-XX","notation":["68-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W01","notation":["68W01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General topics in the theory of algorithms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W05","notation":["68W05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonnumerical algorithms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W10","notation":["68W10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Parallel algorithms in computer science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W15","notation":["68W15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Distributed algorithms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W20","notation":["68W20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Randomized algorithms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W25","notation":["68W25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Approximation algorithms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W27","notation":["68W27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Online algorithms; streaming algorithms"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W30","notation":["68W30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symbolic computation and algebraic computation"},"scopeNote":{"en":["See also 11Yxx, 12-08, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W32","notation":["68W32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algorithms on strings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W35","notation":["68W35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hardware implementations of nonnumerical algorithms (VLSI algorithms, etc.)"},"scopeNote":{"en":["See also 68M07"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W40","notation":["68W40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analysis of algorithms"},"scopeNote":{"en":["See also 68Q25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W50","notation":["68W50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Evolutionary algorithms, genetic algorithms (computational aspects)"},"scopeNote":{"en":["See also 68T05, 68T20, 90C59"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/68W99","notation":["68W99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/68Wxx","notation":["68Wxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mechanics of particles and systems"},"scopeNote":{"en":["For relativistic mechanics, see 83A05, 83C10; for statistical mechanics, see 82-XX"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70-00","notation":["70-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mechanics of particles and systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70-01","notation":["70-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of particles and systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70-02","notation":["70-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70-03","notation":["70-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mechanics of particles and systems"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70-04","notation":["70-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to mechanics of particles and systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70-05","notation":["70-05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Experimental work for problems pertaining to mechanics of particles and systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70-06","notation":["70-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to mechanics of particles and systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70-08","notation":["70-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to mechanics of particles and systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70-10","notation":["70-10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical modeling or simulation for problems pertaining to mechanics of particles and systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70-11","notation":["70-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to mechanics of particles and systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70Axx","notation":["70Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axiomatics, foundations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70A05","notation":["70A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axiomatics, foundations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Axx","notation":["70Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70A99","notation":["70A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Axx","notation":["70Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70Bxx","notation":["70Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kinematics"},"scopeNote":{"en":["See also 53A17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70B05","notation":["70B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kinematics of a particle"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Bxx","notation":["70Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70B10","notation":["70B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kinematics of a rigid body"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Bxx","notation":["70Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70B15","notation":["70B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kinematics of mechanisms and robots"},"scopeNote":{"en":["See also 68T40, 70Q05, 93C85"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Bxx","notation":["70Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70B99","notation":["70B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Bxx","notation":["70Bxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70C99","notation":["70C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Cxx","notation":["70Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70Exx","notation":["70Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamics of a rigid body and of multibody systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70E05","notation":["70E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Motion of the gyroscope"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Exx","notation":["70Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70E15","notation":["70E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free motion of a rigid body"},"scopeNote":{"en":["See also 70M20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Exx","notation":["70Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70E17","notation":["70E17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Motion of a rigid body with a fixed point"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Exx","notation":["70Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70E18","notation":["70E18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Motion of a rigid body in contact with a solid surface"},"scopeNote":{"en":["See also 70F25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Exx","notation":["70Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70E20","notation":["70E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perturbation methods for rigid body dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Exx","notation":["70Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70E40","notation":["70E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integrable cases of motion in rigid body dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Exx","notation":["70Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70E45","notation":["70E45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher-dimensional generalizations in rigid body dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Exx","notation":["70Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70E50","notation":["70E50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability problems in rigid body dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Exx","notation":["70Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70E55","notation":["70E55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamics of multibody systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Exx","notation":["70Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70E60","notation":["70E60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Robot dynamics and control of rigid bodies"},"scopeNote":{"en":["See also 68T40, 70Q05, 93C85"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Exx","notation":["70Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70E99","notation":["70E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Exx","notation":["70Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70Fxx","notation":["70Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamics of a system of particles, including celestial mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70F05","notation":["70F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Two-body problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Fxx","notation":["70Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70F07","notation":["70F07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Three-body problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Fxx","notation":["70Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70F10","notation":["70F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"n-body problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Fxx","notation":["70Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70F15","notation":["70F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Celestial mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Fxx","notation":["70Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70F16","notation":["70F16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Collisions in celestial mechanics, regularization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Fxx","notation":["70Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70F17","notation":["70F17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems for systems of particles"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Fxx","notation":["70Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70F20","notation":["70F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Holonomic systems related to the dynamics of a system of particles"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Fxx","notation":["70Fxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70F35","notation":["70F35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Collision of rigid or pseudo-rigid bodies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Fxx","notation":["70Fxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70F45","notation":["70F45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"The dynamics of infinite particle systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Fxx","notation":["70Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70F99","notation":["70F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Fxx","notation":["70Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70Gxx","notation":["70Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General models, approaches, and methods"},"scopeNote":{"en":["See also 37-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70G10","notation":["70G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Gxx","notation":["70Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70G40","notation":["70G40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological and differential topological methods for problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Gxx","notation":["70Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70G45","notation":["70G45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics"},"scopeNote":{"en":["See also 53Cxx, 53Dxx, 58Axx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Gxx","notation":["70Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70G55","notation":["70G55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algebraic geometry methods for problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Gxx","notation":["70Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70G60","notation":["70G60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems methods for problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Gxx","notation":["70Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70G65","notation":["70G65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symmetries, Lie group and Lie algebra methods for problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Gxx","notation":["70Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70G70","notation":["70G70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Functional analytic methods for problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Gxx","notation":["70Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70G75","notation":["70G75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational methods for problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Gxx","notation":["70Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70G99","notation":["70G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Gxx","notation":["70Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hamiltonian and Lagrangian mechanics"},"scopeNote":{"en":["See also 37Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H03","notation":["70H03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lagrange’s equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H05","notation":["70H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hamilton’s equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H06","notation":["70H06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H07","notation":["70H07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H08","notation":["70H08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nearly integrable Hamiltonian systems, KAM theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H09","notation":["70H09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perturbation theories for problems in Hamiltonian and Lagrangian mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H11","notation":["70H11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H12","notation":["70H12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H14","notation":["70H14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability problems for problems in Hamiltonian and Lagrangian mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H15","notation":["70H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H20","notation":["70H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hamilton-Jacobi equations in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H25","notation":["70H25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hamilton’s principle"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70H30","notation":["70H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other variational principles in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Hxx","notation":["70Hxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70Jxx","notation":["70Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear vibration theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70J10","notation":["70J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modal analysis in linear vibration theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Jxx","notation":["70Jxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70J30","notation":["70J30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free motions in linear vibration theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Jxx","notation":["70Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70J35","notation":["70J35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Forced motions in linear vibration theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Jxx","notation":["70Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70J40","notation":["70J40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Parametric resonances in linear vibration theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Jxx","notation":["70Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70J50","notation":["70J50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Systems arising from the discretization of structural vibration problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Jxx","notation":["70Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70J99","notation":["70J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Jxx","notation":["70Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear dynamics in mechanics"},"scopeNote":{"en":["See also 34Cxx, 37-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70K05","notation":["70K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Phase plane analysis, limit cycles for nonlinear problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70K20","notation":["70K20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability for nonlinear problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70K25","notation":["70K25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free motions for nonlinear problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70K28","notation":["70K28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Parametric resonances for nonlinear problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70K30","notation":["70K30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear resonances for nonlinear problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70K42","notation":["70K42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equilibria and periodic trajectories for nonlinear problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70K45","notation":["70K45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Normal forms for nonlinear problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70K50","notation":["70K50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcations and instability for nonlinear problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70K55","notation":["70K55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics"},"scopeNote":{"en":["See also 37D45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70K60","notation":["70K60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General perturbation schemes for nonlinear problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70K65","notation":["70K65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Averaging of perturbations for nonlinear problems in mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70K75","notation":["70K75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear modes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Kxx","notation":["70Kxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70L10","notation":["70L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic geometric mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Lxx","notation":["70Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70L99","notation":["70L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Lxx","notation":["70Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70Mxx","notation":["70Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orbital mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70M20","notation":["70M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Orbital mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Mxx","notation":["70Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70M99","notation":["70M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Mxx","notation":["70Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70Pxx","notation":["70Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variable mass, rockets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70-XX","notation":["70-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70P05","notation":["70P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variable mass, rockets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Pxx","notation":["70Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70P99","notation":["70P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Pxx","notation":["70Pxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70Q05","notation":["70Q05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Control of mechanical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Qxx","notation":["70Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/70Q99","notation":["70Q99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Qxx","notation":["70Qxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70S05","notation":["70S05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Sxx","notation":["70Sxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70S15","notation":["70S15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Yang-Mills and other gauge theories in mechanics of particles and systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Sxx","notation":["70Sxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/70S99","notation":["70S99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/70Sxx","notation":["70Sxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74-02","notation":["74-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74-03","notation":["74-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mechanics of deformable solids"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74-04","notation":["74-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to mechanics of deformable solids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74-05","notation":["74-05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Experimental work for problems pertaining to mechanics of deformable solids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74-06","notation":["74-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to mechanics of deformable solids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74A10","notation":["74A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stress"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Axx","notation":["74Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74A20","notation":["74A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of constitutive functions in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Axx","notation":["74Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74A60","notation":["74A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Micromechanical theories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Axx","notation":["74Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74Exx","notation":["74Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Material properties given special treatment"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74E20","notation":["74E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Granularity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Exx","notation":["74Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74E25","notation":["74E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Texture in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Exx","notation":["74Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74E30","notation":["74E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Composite and mixture properties"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Exx","notation":["74Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74E35","notation":["74E35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random structure in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Exx","notation":["74Exx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74Fxx","notation":["74Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Coupling of solid mechanics with other effects"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74F05","notation":["74F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Thermal effects in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Fxx","notation":["74Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74F10","notation":["74F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Fxx","notation":["74Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74F15","notation":["74F15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Electromagnetic effects in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Fxx","notation":["74Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74F20","notation":["74F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mixture effects in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Fxx","notation":["74Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74F25","notation":["74F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chemical and reactive effects in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Fxx","notation":["74Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74F99","notation":["74F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Fxx","notation":["74Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equilibrium (steady-state) problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G05","notation":["74G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Explicit solutions of equilibrium problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G10","notation":["74G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G15","notation":["74G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Numerical approximation of solutions of equilibrium problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G25","notation":["74G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence of solutions of equilibrium problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G30","notation":["74G30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Uniqueness of solutions of equilibrium problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G35","notation":["74G35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multiplicity of solutions of equilibrium problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G40","notation":["74G40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Regularity of solutions of equilibrium problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G45","notation":["74G45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bounds for solutions of equilibrium problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G50","notation":["74G50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Saint-Venant’s principle"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G55","notation":["74G55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Qualitative behavior of solutions of equilibrium problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G60","notation":["74G60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bifurcation and buckling"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G65","notation":["74G65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Energy minimization in equilibrium problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G70","notation":["74G70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stress concentrations, singularities in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G75","notation":["74G75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems in equilibrium solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74G99","notation":["74G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Gxx","notation":["74Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H05","notation":["74H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Explicit solutions of dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H10","notation":["74H10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H15","notation":["74H15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Numerical approximation of solutions of dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H20","notation":["74H20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence of solutions of dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H25","notation":["74H25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Uniqueness of solutions of dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H30","notation":["74H30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Regularity of solutions of dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H35","notation":["74H35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H40","notation":["74H40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Long-time behavior of solutions for dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H45","notation":["74H45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vibrations in dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H50","notation":["74H50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random vibrations in dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H55","notation":["74H55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability of dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H60","notation":["74H60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical bifurcation of solutions to dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H65","notation":["74H65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chaotic behavior of solutions to dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H75","notation":["74H75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems in dynamical solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H80","notation":["74H80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Energy minimization in dynamical problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74H99","notation":["74H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Hxx","notation":["74Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74Jxx","notation":["74Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Waves in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74J05","notation":["74J05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear waves in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Jxx","notation":["74Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74J10","notation":["74J10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bulk waves in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Jxx","notation":["74Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74J15","notation":["74J15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Surface waves in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Jxx","notation":["74Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74J20","notation":["74J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Wave scattering in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Jxx","notation":["74Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74J25","notation":["74J25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems for waves in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Jxx","notation":["74Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74J30","notation":["74J30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear waves in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Jxx","notation":["74Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74J35","notation":["74J35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Solitary waves in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Jxx","notation":["74Jxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74J99","notation":["74J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Jxx","notation":["74Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74Kxx","notation":["74Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Thin bodies, structures"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74K05","notation":["74K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Strings"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Kxx","notation":["74Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74K10","notation":["74K10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rods (beams, columns, shafts, arches, rings, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Kxx","notation":["74Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74K15","notation":["74K15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Membranes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Kxx","notation":["74Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74K20","notation":["74K20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Plates"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Kxx","notation":["74Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74K25","notation":["74K25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Shells"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Kxx","notation":["74Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74K30","notation":["74K30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Junctions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Kxx","notation":["74Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74K35","notation":["74K35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Thin films"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Kxx","notation":["74Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74K99","notation":["74K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Kxx","notation":["74Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74Lxx","notation":["74Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special subfields of solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74L05","notation":["74L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geophysical solid mechanics"},"scopeNote":{"en":["See also 86-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Lxx","notation":["74Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74L10","notation":["74L10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Soil and rock mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Lxx","notation":["74Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74L15","notation":["74L15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biomechanical solid mechanics"},"scopeNote":{"en":["See also 92C10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Lxx","notation":["74Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74L99","notation":["74L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Lxx","notation":["74Lxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74Nxx","notation":["74Nxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Phase transformations in solids"},"scopeNote":{"en":["See also 74A50, 80Axx, 82B26, 82C26"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74N05","notation":["74N05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Crystals in solids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Nxx","notation":["74Nxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74N30","notation":["74N30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Problems involving hysteresis in solids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Nxx","notation":["74Nxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74N99","notation":["74N99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Nxx","notation":["74Nxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74P05","notation":["74P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compliance or weight optimization in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Pxx","notation":["74Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74P10","notation":["74P10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Optimization of other properties in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Pxx","notation":["74Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74P15","notation":["74P15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological methods for optimization problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Pxx","notation":["74Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74P20","notation":["74P20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometrical methods for optimization problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Pxx","notation":["74Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74P99","notation":["74P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Pxx","notation":["74Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74Qxx","notation":["74Qxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homogenization, determination of effective properties in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74Q05","notation":["74Q05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homogenization in equilibrium problems of solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Qxx","notation":["74Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74Q10","notation":["74Q10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homogenization and oscillations in dynamical problems of solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Qxx","notation":["74Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74Q15","notation":["74Q15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Effective constitutive equations in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Qxx","notation":["74Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74Q20","notation":["74Q20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bounds on effective properties in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Qxx","notation":["74Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74Q99","notation":["74Q99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Qxx","notation":["74Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74Rxx","notation":["74Rxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fracture and damage"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74-XX","notation":["74-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74R05","notation":["74R05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Brittle damage"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Rxx","notation":["74Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74R10","notation":["74R10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Brittle fracture"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Rxx","notation":["74Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74R15","notation":["74R15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"High-velocity fracture"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Rxx","notation":["74Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74R20","notation":["74R20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Anelastic fracture and damage"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Rxx","notation":["74Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74R99","notation":["74R99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Rxx","notation":["74Rxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74S05","notation":["74S05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite element methods applied to problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Sxx","notation":["74Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74S10","notation":["74S10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite volume methods applied to problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Sxx","notation":["74Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74S15","notation":["74S15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary element methods applied to problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Sxx","notation":["74Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74S20","notation":["74S20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite difference methods applied to problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Sxx","notation":["74Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74S22","notation":["74S22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Isogeometric methods applied to problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Sxx","notation":["74Sxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/74S30","notation":["74S30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other numerical methods applied to problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Sxx","notation":["74Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74S40","notation":["74S40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of fractional calculus in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Sxx","notation":["74Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74S50","notation":["74S50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of graph theory in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Sxx","notation":["74Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74S60","notation":["74S60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic and other probabilistic methods applied to problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Sxx","notation":["74Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74S70","notation":["74S70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complex-variable methods applied to problems in solid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Sxx","notation":["74Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/74S99","notation":["74S99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/74Sxx","notation":["74Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fluid mechanics"},"scopeNote":{"en":["For general continuum mechanics, see 74Axx, or other parts of 74-XX"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/76-01","notation":["76-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76-02","notation":["76-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76-03","notation":["76-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of fluid mechanics"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76-04","notation":["76-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/76-06","notation":["76-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/76-11","notation":["76-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76Axx","notation":["76Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations, constitutive equations, rheology, hydrodynamical models of nonfluid phenomena"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76A02","notation":["76A02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations of fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Axx","notation":["76Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76A05","notation":["76A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Non-Newtonian fluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Axx","notation":["76Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76A10","notation":["76A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Viscoelastic fluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Axx","notation":["76Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76A15","notation":["76A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Liquid crystals"},"scopeNote":{"en":["See also 82D30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Axx","notation":["76Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76A20","notation":["76A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Thin fluid films"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Axx","notation":["76Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76A25","notation":["76A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Superfluids (classical aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Axx","notation":["76Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76A30","notation":["76A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Traffic and pedestrian flow models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Axx","notation":["76Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76A99","notation":["76A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Axx","notation":["76Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Incompressible inviscid fluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76B03","notation":["76B03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence, uniqueness, and regularity theory for incompressible inviscid fluids"},"scopeNote":{"en":["See also 35Q35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76B07","notation":["76B07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Free-surface potential flows for incompressible inviscid fluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76B10","notation":["76B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76B15","notation":["76B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Water waves, gravity waves; dispersion and scattering, nonlinear interaction"},"scopeNote":{"en":["See also 35Q30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76B20","notation":["76B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ship waves"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76B25","notation":["76B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Solitary waves for incompressible inviscid fluids"},"scopeNote":{"en":["See also 35C11"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76B45","notation":["76B45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Capillarity (surface tension) for incompressible inviscid fluids"},"scopeNote":{"en":["See also 76D45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76B47","notation":["76B47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vortex flows for incompressible inviscid fluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76B55","notation":["76B55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Internal waves for incompressible inviscid fluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76B70","notation":["76B70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stratification effects in inviscid fluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76B75","notation":["76B75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Flow control and optimization for incompressible inviscid fluids"},"scopeNote":{"en":["See also 49Q10, 93C20, 93C95"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76B99","notation":["76B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Bxx","notation":["76Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Incompressible viscous fluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D03","notation":["76D03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Existence, uniqueness, and regularity theory for incompressible viscous fluids"},"scopeNote":{"en":["See also 35Q30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D05","notation":["76D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Navier-Stokes equations for incompressible viscous fluids"},"scopeNote":{"en":["See also 35Q30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D06","notation":["76D06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical solutions of Navier-Stokes and related equations"},"scopeNote":{"en":["See also 60H30, 76M35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D07","notation":["76D07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stokes and related (Oseen, etc.) flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D08","notation":["76D08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lubrication theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D09","notation":["76D09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Viscous-inviscid interaction"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D10","notation":["76D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary-layer theory, separation and reattachment, higher-order effects"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D17","notation":["76D17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Viscous vortex flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D25","notation":["76D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Wakes and jets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D27","notation":["76D27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other free boundary flows; Hele-Shaw flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D33","notation":["76D33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Waves for incompressible viscous fluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D45","notation":["76D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Capillarity (surface tension) for incompressible viscous fluids"},"scopeNote":{"en":["See also 76B45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D50","notation":["76D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stratification effects in viscous fluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D55","notation":["76D55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Flow control and optimization for incompressible viscous fluids"},"scopeNote":{"en":["See also 49Q10, 93C20, 93C95"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76D99","notation":["76D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Dxx","notation":["76Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76Exx","notation":["76Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hydrodynamic stability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76E05","notation":["76E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Parallel shear flows in hydrodynamic stability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Exx","notation":["76Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76E06","notation":["76E06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convection in hydrodynamic stability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Exx","notation":["76Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76E07","notation":["76E07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rotation in hydrodynamic stability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Exx","notation":["76Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76E09","notation":["76E09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability and instability of nonparallel flows in hydrodynamic stability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Exx","notation":["76Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76E15","notation":["76E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Absolute and convective instability and stability in hydrodynamic stability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Exx","notation":["76Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76E17","notation":["76E17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Interfacial stability and instability in hydrodynamic stability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Exx","notation":["76Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76E19","notation":["76E19"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compressibility effects in hydrodynamic stability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Exx","notation":["76Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76E20","notation":["76E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability and instability of geophysical and astrophysical flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Exx","notation":["76Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76E25","notation":["76E25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stability and instability of magnetohydrodynamic and electrohydrodynamic flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Exx","notation":["76Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76E30","notation":["76E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear effects in hydrodynamic stability"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Exx","notation":["76Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76E99","notation":["76E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Exx","notation":["76Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Turbulence"},"scopeNote":{"en":["See also 37-XX, 60Gxx, 60Jxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F02","notation":["76F02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fundamentals of turbulence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F05","notation":["76F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Isotropic turbulence; homogeneous turbulence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F06","notation":["76F06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transition to turbulence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F10","notation":["76F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Shear flows and turbulence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F20","notation":["76F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamical systems approach to turbulence"},"scopeNote":{"en":["See also 37-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F25","notation":["76F25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Turbulent transport, mixing"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F30","notation":["76F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Renormalization and other field-theoretical methods for turbulence"},"scopeNote":{"en":["See also 81T99"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F35","notation":["76F35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convective turbulence"},"scopeNote":{"en":["See also 76E15, 76Rxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F40","notation":["76F40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Turbulent boundary layers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F45","notation":["76F45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stratification effects in turbulence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F50","notation":["76F50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Compressibility effects in turbulence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F55","notation":["76F55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical turbulence modeling"},"scopeNote":{"en":["See also 76M35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F60","notation":["76F60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"k-ε modeling in turbulence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F65","notation":["76F65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Direct numerical and large eddy simulation of turbulence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F70","notation":["76F70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Control of turbulent flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F80","notation":["76F80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Turbulent combustion; reactive turbulence"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76F99","notation":["76F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Fxx","notation":["76Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76Gxx","notation":["76Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General aerodynamics and subsonic flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76G25","notation":["76G25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General aerodynamics and subsonic flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Gxx","notation":["76Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76G99","notation":["76G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Gxx","notation":["76Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76Hxx","notation":["76Hxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transonic flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76H05","notation":["76H05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transonic flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Hxx","notation":["76Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76H99","notation":["76H99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Hxx","notation":["76Hxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76Jxx","notation":["76Jxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Supersonic flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76J20","notation":["76J20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Supersonic flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Jxx","notation":["76Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76J99","notation":["76J99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Jxx","notation":["76Jxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76Kxx","notation":["76Kxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hypersonic flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76K05","notation":["76K05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hypersonic flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Kxx","notation":["76Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76K99","notation":["76K99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Kxx","notation":["76Kxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76Lxx","notation":["76Lxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Shock waves and blast waves in fluid mechanics"},"scopeNote":{"en":["See also 35L67"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76L05","notation":["76L05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Shock waves and blast waves in fluid mechanics"},"scopeNote":{"en":["See also 35L67"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Lxx","notation":["76Lxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76L99","notation":["76L99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Lxx","notation":["76Lxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/76M10","notation":["76M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite element methods applied to problems in fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Mxx","notation":["76Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76M12","notation":["76M12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite volume methods applied to problems in fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Mxx","notation":["76Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76M15","notation":["76M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary element methods applied to problems in fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Mxx","notation":["76Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76M20","notation":["76M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite difference methods applied to problems in fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Mxx","notation":["76Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76M21","notation":["76M21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems in fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Mxx","notation":["76Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76M22","notation":["76M22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral methods applied to problems in fluid mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Mxx","notation":["76Mxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/76R05","notation":["76R05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Forced convection"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Rxx","notation":["76Rxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/76T05","notation":["76T05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Liquid-liquid two component flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Txx","notation":["76Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76T10","notation":["76T10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Liquid-gas two-phase flows, bubbly flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Txx","notation":["76Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76T15","notation":["76T15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dusty-gas two-phase flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Txx","notation":["76Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76T17","notation":["76T17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Two gas multicomponent flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Txx","notation":["76Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76T20","notation":["76T20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Suspensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Txx","notation":["76Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76T25","notation":["76T25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Granular flows"},"scopeNote":{"en":["See also 74C99, 74E20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Txx","notation":["76Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76T30","notation":["76T30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Three or more component flows"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Txx","notation":["76Txx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/76Uxx","notation":["76Uxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rotating fluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76-XX","notation":["76-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76U05","notation":["76U05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rotating fluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Uxx","notation":["76Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76U60","notation":["76U60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geophysical flows"},"scopeNote":{"en":["See also 86A05, 86A10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Uxx","notation":["76Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/76U65","notation":["76U65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rossby waves"},"scopeNote":{"en":["See also 86A05, 86A10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Uxx","notation":["76Uxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/76Y05","notation":["76Y05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum hydrodynamics and relativistic hydrodynamics"},"scopeNote":{"en":["See also 82D50, 83C55, 85A30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Yxx","notation":["76Yxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/76Z05","notation":["76Z05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Physiological flows"},"scopeNote":{"en":["See also 92C35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Zxx","notation":["76Zxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/76Z99","notation":["76Z99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/76Zxx","notation":["76Zxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/78-02","notation":["78-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78-XX","notation":["78-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78-03","notation":["78-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of optics and electromagnetic theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78-XX","notation":["78-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78-04","notation":["78-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78-XX","notation":["78-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/78-06","notation":["78-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78-XX","notation":["78-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/78-11","notation":["78-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78-XX","notation":["78-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/78A02","notation":["78A02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A05","notation":["78A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometric optics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A10","notation":["78A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Physical optics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A15","notation":["78A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Electron optics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A20","notation":["78A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Space charge waves"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A25","notation":["78A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Electromagnetic theory, general"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A30","notation":["78A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Electro- and magnetostatics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A35","notation":["78A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Motion of charged particles"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A37","notation":["78A37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ion traps"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A40","notation":["78A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Waves and radiation in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A45","notation":["78A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Diffraction, scattering"},"scopeNote":{"en":["For WKB methods see 34E20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A46","notation":["78A46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems (including inverse scattering) in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A48","notation":["78A48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Composite media; random media in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A50","notation":["78A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Antennas, waveguides in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A55","notation":["78A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Technical applications of optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A57","notation":["78A57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Electrochemistry"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A60","notation":["78A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lasers, masers, optical bistability, nonlinear optics"},"scopeNote":{"en":["See also 81V80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A70","notation":["78A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biological applications of optics and electromagnetic theory"},"scopeNote":{"en":["See also 91D30, 92C30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A97","notation":["78A97"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in Section 78)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78A99","notation":["78A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Axx","notation":["78Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Basic methods for problems in optics and electromagnetic theory"},"scopeNote":{"en":["See also 65-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78-XX","notation":["78-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78M05","notation":["78M05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Method of moments applied to problems in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/78M16","notation":["78M16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multipole methods applied to problems in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78M20","notation":["78M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite difference methods applied to problems in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78M22","notation":["78M22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral, collocation and related methods applied to problems in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78M25","notation":["78M25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other numerical methods applied to problems in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78M30","notation":["78M30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational methods applied to problems in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78M31","notation":["78M31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monte Carlo methods applied to problems in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78M32","notation":["78M32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Neural and heuristic methods applied to problems in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78M34","notation":["78M34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Model reduction in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78M35","notation":["78M35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic analysis in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/78M40","notation":["78M40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Homogenization in optics and electromagnetic theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/78M99","notation":["78M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/78Mxx","notation":["78Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80-XX","notation":["80-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical thermodynamics, heat transfer"},"scopeNote":{"en":["For thermodynamics of solids, see 74A15"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/80-01","notation":["80-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to classical thermodynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80-XX","notation":["80-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/80-03","notation":["80-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of classical thermodynamics"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80-XX","notation":["80-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80-04","notation":["80-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to classical thermodynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80-XX","notation":["80-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80-05","notation":["80-05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Experimental work for problems pertaining to classical thermodynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80-XX","notation":["80-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80-06","notation":["80-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to classical thermodynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80-XX","notation":["80-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/80-11","notation":["80-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to classical thermodynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80-XX","notation":["80-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80Axx","notation":["80Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Thermodynamics and heat transfer"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80-XX","notation":["80-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80A05","notation":["80A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations of thermodynamics and heat transfer"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Axx","notation":["80Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80A10","notation":["80A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical and relativistic thermodynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Axx","notation":["80Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80A17","notation":["80A17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Thermodynamics of continua"},"scopeNote":{"en":["See also 74A15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Axx","notation":["80Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80A20","notation":["80A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Diffusive and convective heat and mass transfer, heat flow"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Axx","notation":["80Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80A22","notation":["80A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stefan problems, phase changes, etc."},"scopeNote":{"en":["See also 74Nxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Axx","notation":["80Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80A23","notation":["80A23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems in thermodynamics and heat transfer"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Axx","notation":["80Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80A25","notation":["80A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combustion"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Axx","notation":["80Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/80A32","notation":["80A32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chemically reacting flows"},"scopeNote":{"en":["See also 92C45, 92E20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Axx","notation":["80Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80A50","notation":["80A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chemistry (general) in thermodynamics and heat transfer"},"scopeNote":{"en":["See mainly 92Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Axx","notation":["80Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80A60","notation":["80A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Radiative heat transfer"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Axx","notation":["80Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/80Mxx","notation":["80Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Basic methods in thermodynamics and heat transfer"},"scopeNote":{"en":["See also 65-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80-XX","notation":["80-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/80M20","notation":["80M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite difference methods applied to problems in thermodynamics and heat transfer"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Mxx","notation":["80Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80M22","notation":["80M22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral, collocation and related (meshless) methods applied to problems in thermodynamics and heat transfer"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Mxx","notation":["80Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80M25","notation":["80M25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other numerical methods applied to problems in thermodynamics and heat transfer"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Mxx","notation":["80Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80M30","notation":["80M30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational methods applied to problems in thermodynamics and heat transfer"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Mxx","notation":["80Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80M31","notation":["80M31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monte Carlo methods applied to problems in thermodynamics and heat transfer"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Mxx","notation":["80Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/80M35","notation":["80M35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic analysis for problems in thermodynamics and heat transfer"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Mxx","notation":["80Mxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/80M99","notation":["80M99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/80Mxx","notation":["80Mxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/81-01","notation":["81-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81-02","notation":["81-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81-03","notation":["81-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of quantum theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81-04","notation":["81-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/81-06","notation":["81-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81-08","notation":["81-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81-10","notation":["81-10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical modeling or simulation for problems pertaining to quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81-11","notation":["81-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations, quantum information and its processing, quantum axioms, and philosophy"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P05","notation":["81P05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General and philosophical questions in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P10","notation":["81P10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)"},"scopeNote":{"en":["See also 03G12, 06C15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P13","notation":["81P13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Contextuality in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P15","notation":["81P15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum measurement theory, state operations, state preparations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P16","notation":["81P16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum state spaces, operational and probabilistic concepts"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P17","notation":["81P17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum entropies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P18","notation":["81P18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum state tomography, quantum state discrimination"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P20","notation":["81P20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic mechanics (including stochastic electrodynamics)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P40","notation":["81P40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum coherence, entanglement, quantum correlations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P42","notation":["81P42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Entanglement measures, concurrencies, separability criteria"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P43","notation":["81P43"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum discord"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P45","notation":["81P45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum information, communication, networks (quantum-theoretic aspects)"},"scopeNote":{"en":["See also 94A15, 94A17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P47","notation":["81P47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum channels, fidelity"},"scopeNote":{"en":["See also 94A40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P48","notation":["81P48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"LOCC, teleportation, dense coding, remote state operations, distillation"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P50","notation":["81P50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum state estimation, approximate cloning"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P55","notation":["81P55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special bases (entangled, mutual unbiased, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P65","notation":["81P65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum gates"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P68","notation":["81P68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum computation"},"scopeNote":{"en":["See also 68Q09; For algorithmic aspects, see 68Q12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P70","notation":["81P70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum coding (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P73","notation":["81P73"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational stability and error-correcting codes for quantum computation and communication processing"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P94","notation":["81P94"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum cryptography (quantum-theoretic aspects)"},"scopeNote":{"en":["See also 94A60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81P99","notation":["81P99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Pxx","notation":["81Pxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General mathematical topics and methods in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q05","notation":["81Q05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q10","notation":["81Q10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Selfadjoint operator theory in quantum theory, including spectral analysis"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q12","notation":["81Q12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonselfadjoint operator theory in quantum theory including creation and destruction operators"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q15","notation":["81Q15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perturbation theories for operators and differential equations in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q20","notation":["81Q20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q30","notation":["81Q30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Feynman integrals and graphs; applications of algebraic topology and algebraic geometry"},"scopeNote":{"en":["See also 14D05, 32S40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q35","notation":["81Q35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices"},"scopeNote":{"en":["See also 81R20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q37","notation":["81Q37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum dots, waveguides, ratchets, etc."},"scopeNote":{"en":["See also 82D20, 82D77"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q40","notation":["81Q40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bethe-Salpeter and other integral equations arising in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q50","notation":["81Q50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum chaos"},"scopeNote":{"en":["See also 37Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q60","notation":["81Q60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Supersymmetry and quantum mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q65","notation":["81Q65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Alternative quantum mechanics (including hidden variables, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q70","notation":["81Q70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q80","notation":["81Q80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special quantum systems, such as solvable systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Q93","notation":["81Q93"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum control"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Qxx","notation":["81Qxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/81Rxx","notation":["81Rxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groups and algebras in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81R05","notation":["81R05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite-dimensional groups and algebras motivated by physics and their representations"},"scopeNote":{"en":["See also 20C35, 22E70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Rxx","notation":["81Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81R10","notation":["81R10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, W -algebras and other current algebras and their representations"},"scopeNote":{"en":["See also 17B65, 17B67, 22E65, 22E67, 22E70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Rxx","notation":["81Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81R12","notation":["81R12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Groups and algebras in quantum theory and relations with integrable systems"},"scopeNote":{"en":["See also 17Bxx, 37J35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Rxx","notation":["81Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81R15","notation":["81R15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operator algebra methods applied to problems in quantum theory"},"scopeNote":{"en":["See also 46Lxx, 81T05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Rxx","notation":["81Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81R20","notation":["81R20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Covariant wave equations in quantum theory, relativistic quantum mechanics"},"scopeNote":{"en":["See also 81Q35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Rxx","notation":["81Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81R25","notation":["81R25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spinor and twistor methods applied to problems in quantum theory"},"scopeNote":{"en":["See also 32L25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Rxx","notation":["81Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81R30","notation":["81R30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Coherent states ; squeezed states in quantum theory"},"scopeNote":{"en":["See also 22E45; See also 81V80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Rxx","notation":["81Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81R40","notation":["81R40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Symmetry breaking in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Rxx","notation":["81Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81R50","notation":["81R50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum groups and related algebraic methods applied to problems in quantum theory"},"scopeNote":{"en":["See also 16T20, 17B37"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Rxx","notation":["81Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81R60","notation":["81R60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative geometry in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Rxx","notation":["81Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81R99","notation":["81R99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Rxx","notation":["81Rxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Sxx","notation":["81Sxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General quantum mechanics and problems of quantization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81S05","notation":["81S05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Commutation relations and statistics as related to quantum mechanics (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Sxx","notation":["81Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81S07","notation":["81S07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Uncertainty relations, also entropic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Sxx","notation":["81Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81S08","notation":["81S08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Canonical quantization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Sxx","notation":["81Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81S10","notation":["81S10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometry and quantization, symplectic methods"},"scopeNote":{"en":["See also 53D50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Sxx","notation":["81Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81S20","notation":["81S20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic quantization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Sxx","notation":["81Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81S22","notation":["81S22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Open systems, reduced dynamics, master equations, decoherence"},"scopeNote":{"en":["See also 82C31"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Sxx","notation":["81Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81S25","notation":["81S25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum stochastic calculus"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Sxx","notation":["81Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81S30","notation":["81S30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Sxx","notation":["81Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81S40","notation":["81S40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Path integrals in quantum mechanics"},"scopeNote":{"en":["See also 58D30, 81Q30, 81T18"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Sxx","notation":["81Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81S99","notation":["81S99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Sxx","notation":["81Sxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum field theory; related classical field theories"},"scopeNote":{"en":["See also 70Sxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T05","notation":["81T05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Axiomatic quantum field theory; operator algebras"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T08","notation":["81T08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Constructive quantum field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T10","notation":["81T10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Model quantum field theories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T11","notation":["81T11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Higher spin theories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T12","notation":["81T12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Effective quantum field theories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T13","notation":["81T13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Yang-Mills and other gauge theories in quantum field theory"},"scopeNote":{"en":["See also 53C07, 58E15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T15","notation":["81T15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Perturbative methods of renormalization applied to problems in quantum field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T16","notation":["81T16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonperturbative methods of renormalization applied to problems in quantum field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T17","notation":["81T17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Renormalization group methods applied to problems in quantum field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T18","notation":["81T18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Feynman diagrams"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T20","notation":["81T20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum field theory on curved space or space-time backgrounds"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T25","notation":["81T25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum field theory on lattices"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T27","notation":["81T27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuum limits in quantum field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T28","notation":["81T28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Thermal quantum field theory"},"scopeNote":{"en":["See also 82B30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T30","notation":["81T30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"String and superstring theories; other extended objects (e.g., branes) in quantum field theory"},"scopeNote":{"en":["See also 83E30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T32","notation":["81T32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matrix models and tensor models for quantum field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T33","notation":["81T33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dimensional compactification in quantum field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T35","notation":["81T35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Correspondence, duality, holography (ADS/CFT, gauge/gravity, etc.)"},"scopeNote":{"en":["See also 83E05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T40","notation":["81T40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Two-dimensional field theories, conformal field theories, etc. in quantum mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T45","notation":["81T45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Topological field theories in quantum mechanics"},"scopeNote":{"en":["See also 57R56, 58Dxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T50","notation":["81T50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Anomalies in quantum field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T55","notation":["81T55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Casimir effect in quantum field theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T60","notation":["81T60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Supersymmetric field theories in quantum mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T70","notation":["81T70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantization in field theory; cohomological methods"},"scopeNote":{"en":["See also 58D29"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T75","notation":["81T75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncommutative geometry methods in quantum field theory"},"scopeNote":{"en":["See also 46L85, 46L87, 58B34"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81T99","notation":["81T99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Txx","notation":["81Txx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Uxx","notation":["81Uxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum scattering theory"},"scopeNote":{"en":["See also 34A55, 34L25, 34L40, 35P25, 47A40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81U05","notation":["81U05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"2-body potential quantum scattering theory"},"scopeNote":{"en":["For WKB methods, see also 34E20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Uxx","notation":["81Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81U10","notation":["81U10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"n-body potential quantum scattering theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Uxx","notation":["81Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81U15","notation":["81U15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exactly and quasi-solvable systems arising in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Uxx","notation":["81Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81U20","notation":["81U20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"S-matrix theory, etc. in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Uxx","notation":["81Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81U24","notation":["81U24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Resonances in quantum scattering theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Uxx","notation":["81Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81U26","notation":["81U26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Tunneling in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Uxx","notation":["81Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81U30","notation":["81U30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dispersion theory, dispersion relations arising in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Uxx","notation":["81Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81U35","notation":["81U35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inelastic and multichannel quantum scattering"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Uxx","notation":["81Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81U40","notation":["81U40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse scattering problems in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Uxx","notation":["81Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81U90","notation":["81U90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Particle decays in scattering"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Uxx","notation":["81Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81U99","notation":["81U99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Uxx","notation":["81Uxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of quantum theory to specific physical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81-XX","notation":["81-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V05","notation":["81V05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Strong interaction, including quantum chromodynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V10","notation":["81V10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Electromagnetic interaction; quantum electrodynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V15","notation":["81V15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Weak interaction in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V17","notation":["81V17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gravitational interaction in quantum theory"},"scopeNote":{"en":["See also 83Cxx, 83Exx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V19","notation":["81V19"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other fundamental interactions in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V22","notation":["81V22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unified quantum theories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V25","notation":["81V25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other elementary particle theory in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V27","notation":["81V27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Anyons"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V35","notation":["81V35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nuclear physics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V45","notation":["81V45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Atomic physics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V55","notation":["81V55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Molecular physics"},"scopeNote":{"en":["See also 92E10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V60","notation":["81V60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mono-, di- and multipole moments (EM and other), gyromagnetic relations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V65","notation":["81V65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum dots as quasi particles"},"scopeNote":{"en":["See also 82D20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V70","notation":["81V70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Many-body theory; quantum Hall effect"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V72","notation":["81V72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Particle exchange symmetries in quantum theory (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V73","notation":["81V73"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bosonic systems in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V74","notation":["81V74"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fermionic systems in quantum theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V80","notation":["81V80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum optics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/81V99","notation":["81V99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/81Vxx","notation":["81Vxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanics, structure of matter"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82-00","notation":["82-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82-01","notation":["82-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82-02","notation":["82-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82-03","notation":["82-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of statistical mechanics"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82-04","notation":["82-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82-05","notation":["82-05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Experimental work for problems pertaining to statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82-06","notation":["82-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82-10","notation":["82-10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical modeling or simulation for problems pertaining to statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82-11","notation":["82-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equilibrium statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B03","notation":["82B03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations of equilibrium statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B05","notation":["82B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical equilibrium statistical mechanics (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B10","notation":["82B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum equilibrium statistical mechanics (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B20","notation":["82B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B21","notation":["82B21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B23","notation":["82B23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exactly solvable models; Bethe ansatz"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B24","notation":["82B24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B26","notation":["82B26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Phase transitions (general) in equilibrium statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B27","notation":["82B27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Critical phenomena in equilibrium statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B28","notation":["82B28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Renormalization group methods in equilibrium statistical mechanics"},"scopeNote":{"en":["See also 81T17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B30","notation":["82B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical thermodynamics"},"scopeNote":{"en":["See also 80-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B31","notation":["82B31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic methods applied to problems in equilibrium statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B35","notation":["82B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Irreversible thermodynamics, including Onsager-Machlup theory"},"scopeNote":{"en":["See also 92E20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B40","notation":["82B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kinetic theory of gases in equilibrium statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B41","notation":["82B41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics"},"scopeNote":{"en":["See also 60G50, 82C41"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B43","notation":["82B43"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Percolation"},"scopeNote":{"en":["See also 60K35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B44","notation":["82B44"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82B99","notation":["82B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Bxx","notation":["82Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Time-dependent statistical mechanics (dynamic and nonequilibrium)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C03","notation":["82C03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Foundations of time-dependent statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C05","notation":["82C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical dynamic and nonequilibrium statistical mechanics (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C10","notation":["82C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum dynamics and nonequilibrium statistical mechanics (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C20","notation":["82C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C21","notation":["82C21"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C22","notation":["82C22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Interacting particle systems in time-dependent statistical mechanics"},"scopeNote":{"en":["See also 60K35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C23","notation":["82C23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exactly solvable dynamic models in time-dependent statistical mechanics"},"scopeNote":{"en":["See also 37K60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C24","notation":["82C24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C26","notation":["82C26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamic and nonequilibrium phase transitions (general) in statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C27","notation":["82C27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamic critical phenomena in statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C28","notation":["82C28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics"},"scopeNote":{"en":["See also 81T17"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C31","notation":["82C31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics"},"scopeNote":{"en":["See also 60H10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C32","notation":["82C32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Neural nets applied to problems in time-dependent statistical mechanics"},"scopeNote":{"en":["See also 68T05, 91E40, 92B20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C35","notation":["82C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Irreversible thermodynamics, including Onsager-Machlup theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C40","notation":["82C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kinetic theory of gases in time-dependent statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C41","notation":["82C41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics"},"scopeNote":{"en":["See also 60G50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C43","notation":["82C43"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Time-dependent percolation in statistical mechanics"},"scopeNote":{"en":["See also 60K35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C44","notation":["82C44"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C70","notation":["82C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transport processes in time-dependent statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82C99","notation":["82C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Cxx","notation":["82Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of statistical mechanics to specific types of physical systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D03","notation":["82D03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies in condensed matter (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D05","notation":["82D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of gases"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D10","notation":["82D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of plasmas"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D15","notation":["82D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of liquids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D20","notation":["82D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of solids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D25","notation":["82D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of crystals"},"scopeNote":{"en":["For crystallographic group theory, see 20H15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D30","notation":["82D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D35","notation":["82D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of metals"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D37","notation":["82D37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of semiconductors"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D40","notation":["82D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of magnetic materials"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D45","notation":["82D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of ferroelectrics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D50","notation":["82D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of superfluids"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D55","notation":["82D55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of superconductors"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D60","notation":["82D60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of polymers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D75","notation":["82D75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nuclear reactor theory; neutron transport"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D77","notation":["82D77"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum waveguides, quantum wires"},"scopeNote":{"en":["See also 78A50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D80","notation":["82D80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical mechanical studies of nanostructures and nanoparticles"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82D99","notation":["82D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Dxx","notation":["82Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82Mxx","notation":["82Mxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Basic methods in statistical mechanics"},"scopeNote":{"en":["See also 65-XX"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82-XX","notation":["82-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82M10","notation":["82M10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite element, Galerkin and related methods applied to problems in statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Mxx","notation":["82Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82M12","notation":["82M12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite volume methods applied to problems in statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Mxx","notation":["82Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82M15","notation":["82M15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boundary element methods applied to problems in statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Mxx","notation":["82Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82M20","notation":["82M20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Finite difference methods applied to problems in statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Mxx","notation":["82Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82M22","notation":["82M22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spectral, collocation and related (meshless) methods applied to problems in statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Mxx","notation":["82Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82M25","notation":["82M25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other numerical methods applied to problems in statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Mxx","notation":["82Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82M30","notation":["82M30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Variational methods applied to problems in statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Mxx","notation":["82Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82M31","notation":["82M31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Monte Carlo methods applied to problems in statistical mechanics"},"scopeNote":{"en":["See also 65C05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Mxx","notation":["82Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82M36","notation":["82M36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational density functional analysis in statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Mxx","notation":["82Mxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/82M37","notation":["82M37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational molecular dynamics in statistical mechanics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/82Mxx","notation":["82Mxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/83-06","notation":["83-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83-XX","notation":["83-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83-08","notation":["83-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83-XX","notation":["83-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83-10","notation":["83-10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical modeling or simulation for problems pertaining to relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83-XX","notation":["83-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83-11","notation":["83-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83-XX","notation":["83-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83Axx","notation":["83Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special relativity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83-XX","notation":["83-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83A05","notation":["83A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special relativity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Axx","notation":["83Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83A99","notation":["83A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Axx","notation":["83Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83Bxx","notation":["83Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Observational and experimental questions in relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83-XX","notation":["83-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83B05","notation":["83B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Observational and experimental questions in relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Bxx","notation":["83Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83B99","notation":["83B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Bxx","notation":["83Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General relativity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83-XX","notation":["83-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C05","notation":["83C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Einstein’s equations (general structure, canonical formalism, Cauchy problems)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C10","notation":["83C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equations of motion in general relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C15","notation":["83C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Exact solutions to problems in general relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C20","notation":["83C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C22","notation":["83C22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Einstein-Maxwell equations"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C25","notation":["83C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Approximation procedures, weak fields in general relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C27","notation":["83C27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C30","notation":["83C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Asymptotic procedures (radiation, news functions, H-spaces, etc.) in general relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C35","notation":["83C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gravitational waves"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C40","notation":["83C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Gravitational energy and conservation laws; groups of motions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C45","notation":["83C45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantization of the gravitational field"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C47","notation":["83C47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methods of quantum field theory in general relativity and gravitational theory"},"scopeNote":{"en":["See also 81T20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C50","notation":["83C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Electromagnetic fields in general relativity and gravitational theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C55","notation":["83C55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C56","notation":["83C56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dark matter and dark energy"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C57","notation":["83C57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Black holes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C60","notation":["83C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C65","notation":["83C65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methods of noncommutative geometry in general relativity"},"scopeNote":{"en":["See also 58B34"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C75","notation":["83C75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Space-time singularities, cosmic censorship, etc."},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C80","notation":["83C80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analogues of general relativity in lower dimensions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83C99","notation":["83C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Cxx","notation":["83Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83Dxx","notation":["83Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Relativistic gravitational theories other than Einstein’s, including asymmetric field theories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83-XX","notation":["83-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/83Exx","notation":["83Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Unified, higher-dimensional and super field theories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83-XX","notation":["83-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83E05","notation":["83E05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometrodynamics and the holographic principle"},"scopeNote":{"en":["See also 81T35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Exx","notation":["83Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83E15","notation":["83E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kaluza-Klein and other higher-dimensional theories"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Exx","notation":["83Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83E30","notation":["83E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"String and superstring theories in gravitational theory"},"scopeNote":{"en":["See also 81T30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Exx","notation":["83Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83E50","notation":["83E50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Supergravity"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Exx","notation":["83Exx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/83Fxx","notation":["83Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cosmology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83-XX","notation":["83-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83F05","notation":["83F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cosmology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Fxx","notation":["83Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/83F99","notation":["83F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/83Fxx","notation":["83Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/85-XX","notation":["85-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Astronomy and astrophysics"},"scopeNote":{"en":["For celestial mechanics, see 70F15"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/85-00","notation":["85-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to astronomy and astrophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85-XX","notation":["85-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/85-03","notation":["85-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of astronomy and astrophysics"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85-XX","notation":["85-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/85-05","notation":["85-05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Experimental work for problems pertaining to astronomy and astrophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85-XX","notation":["85-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/85-06","notation":["85-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to astronomy and astrophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85-XX","notation":["85-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/85-08","notation":["85-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to astronomy and astrophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85-XX","notation":["85-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/85-10","notation":["85-10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical modeling or simulation for problems pertaining to astronomy and astrophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85-XX","notation":["85-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/85-11","notation":["85-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to astronomy and astrophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85-XX","notation":["85-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/85Axx","notation":["85Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Astronomy and astrophysics"},"scopeNote":{"en":["For celestial mechanics, see 70F15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85-XX","notation":["85-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/85A04","notation":["85A04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General questions in astronomy and astrophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85Axx","notation":["85Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/85A05","notation":["85A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Galactic and stellar dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85Axx","notation":["85Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/85A15","notation":["85A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Galactic and stellar structure"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85Axx","notation":["85Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/85A20","notation":["85A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Planetary atmospheres"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85Axx","notation":["85Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/85A35","notation":["85A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical astronomy"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/85Axx","notation":["85Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/86-01","notation":["86-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86-XX","notation":["86-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/86-03","notation":["86-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of geophysics"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86-XX","notation":["86-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86-04","notation":["86-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to geophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86-XX","notation":["86-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/86-06","notation":["86-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to geophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86-XX","notation":["86-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86-08","notation":["86-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to geophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86-XX","notation":["86-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/86-11","notation":["86-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to geophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86-XX","notation":["86-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/86A04","notation":["86A04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General questions in geophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86A05","notation":["86A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hydrology, hydrography, oceanography"},"scopeNote":{"en":["See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86A08","notation":["86A08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Climate science and climate modeling"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/86A15","notation":["86A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Seismology (including tsunami modeling), earthquakes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86A20","notation":["86A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Potentials, prospecting"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86A22","notation":["86A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inverse problems in geophysics"},"scopeNote":{"en":["See also 35R30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86A25","notation":["86A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geo-electricity and geomagnetism"},"scopeNote":{"en":["See also 76W05, 78A25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86A30","notation":["86A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geodesy, mapping problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86A32","notation":["86A32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geostatistics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86A40","notation":["86A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Glaciology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86A60","notation":["86A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geological problems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86A70","notation":["86A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Vulcanology; magma and lava flow"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/86A99","notation":["86A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/86Axx","notation":["86Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90-XX","notation":["90-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operations research, mathematical programming"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/90-04","notation":["90-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to operations research and mathematical programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90-XX","notation":["90-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90-05","notation":["90-05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Experimental work for problems pertaining to operations research and mathematical programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90-XX","notation":["90-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90-06","notation":["90-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to operations research and mathematical programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90-XX","notation":["90-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90-08","notation":["90-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to operations research and mathematical programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90-XX","notation":["90-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/90-11","notation":["90-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to operations research and mathematical programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90-XX","notation":["90-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Operations research and management science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90-XX","notation":["90-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90B05","notation":["90B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Inventory, storage, reservoirs"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90B06","notation":["90B06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transportation, logistics and supply chain management"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90B10","notation":["90B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Deterministic network models in operations research"},"scopeNote":{"en":["For network control, see 93B70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90B15","notation":["90B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic network models in operations research"},"scopeNote":{"en":["For network control, see 93B70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90B18","notation":["90B18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Communication networks in operations research"},"scopeNote":{"en":["See also 68M10, 68M12, 68M18, 94A05; For networks as computational models, see 68Q06"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/90B25","notation":["90B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Reliability, availability, maintenance, inspection in operations research"},"scopeNote":{"en":["See also 60K10, 62N05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90B30","notation":["90B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Production models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/90B36","notation":["90B36"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic scheduling theory in operations research"},"scopeNote":{"en":["See also 68M20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90B40","notation":["90B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Search theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90B50","notation":["90B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Management decision making, including multiple objectives"},"scopeNote":{"en":["See also 90C29, 90C31, 91A35, 91B06"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90B60","notation":["90B60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Marketing, advertising"},"scopeNote":{"en":["See also 91B60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90B70","notation":["90B70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of organizations, manpower planning in operations research"},"scopeNote":{"en":["See also 91D35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90B80","notation":["90B80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discrete location and assignment"},"scopeNote":{"en":["See also 90C10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90B85","notation":["90B85"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Continuous location"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/90B99","notation":["90B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Bxx","notation":["90Bxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/90C05","notation":["90C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linear programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C06","notation":["90C06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Large-scale problems in mathematical programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C08","notation":["90C08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C09","notation":["90C09"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boolean programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C10","notation":["90C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Integer programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C11","notation":["90C11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mixed integer programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C15","notation":["90C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C17","notation":["90C17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Robustness in mathematical programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C20","notation":["90C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quadratic programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C22","notation":["90C22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semidefinite programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C23","notation":["90C23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polynomial optimization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C24","notation":["90C24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Tropical optimization (e.g., max-plus optimization)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C25","notation":["90C25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Convex programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C26","notation":["90C26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonconvex programming, global optimization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C27","notation":["90C27"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial optimization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C29","notation":["90C29"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multi-objective and goal programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C30","notation":["90C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Nonlinear programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C31","notation":["90C31"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sensitivity, stability, parametric optimization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C32","notation":["90C32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fractional programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C33","notation":["90C33"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C34","notation":["90C34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Semi-infinite programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C35","notation":["90C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Programming involving graphs or networks"},"scopeNote":{"en":["See also 90C27"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C39","notation":["90C39"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamic programming"},"scopeNote":{"en":["See also 49L20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C40","notation":["90C40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Markov and semi-Markov decision processes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C46","notation":["90C46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Optimality conditions and duality in mathematical programming"},"scopeNote":{"en":["See also 49N15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C47","notation":["90C47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Minimax problems in mathematical programming"},"scopeNote":{"en":["See also 49K35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C48","notation":["90C48"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Programming in abstract spaces"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C49","notation":["90C49"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Extreme-point and pivoting methods"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C51","notation":["90C51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Interior-point methods"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C52","notation":["90C52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methods of reduced gradient type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C53","notation":["90C53"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methods of quasi-Newton type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C55","notation":["90C55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Methods of successive quadratic programming type"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C56","notation":["90C56"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Derivative-free methods and methods using generalized derivatives"},"scopeNote":{"en":["See also 49J52"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C57","notation":["90C57"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Polyhedral combinatorics, branch-and-bound, branch-and-cut"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C59","notation":["90C59"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Approximation methods and heuristics in mathematical programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C60","notation":["90C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Abstract computational complexity for mathematical programming problems"},"scopeNote":{"en":["See also 68Q25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C70","notation":["90C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy and other nonstochastic uncertainty mathematical programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C90","notation":["90C90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of mathematical programming"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/90C99","notation":["90C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/90Cxx","notation":["90Cxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/91-02","notation":["91-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91-XX","notation":["91-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/91-08","notation":["91-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to game theory, economics, and finance"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91-XX","notation":["91-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/91A05","notation":["91A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"2-person games"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A06","notation":["91A06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"n-person games, n > 2"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A07","notation":["91A07"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Games with infinitely many players"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A10","notation":["91A10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Noncooperative games"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A11","notation":["91A11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Equilibrium refinements"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A12","notation":["91A12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cooperative games"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A14","notation":["91A14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Potential and congestion games"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A15","notation":["91A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic games, stochastic differential games"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A16","notation":["91A16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mean field games (aspects of game theory)"},"scopeNote":{"en":["See also 35Q89, 49N80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A18","notation":["91A18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Games in extensive form"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A20","notation":["91A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multistage and repeated games"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A22","notation":["91A22"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Evolutionary games"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A23","notation":["91A23"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Differential games (aspects of game theory)"},"scopeNote":{"en":["See also 49N70"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A24","notation":["91A24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Positional games (pursuit and evasion, etc.)"},"scopeNote":{"en":["See also 49N75"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A25","notation":["91A25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamic games"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/91A28","notation":["91A28"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Signaling and communication in game theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A30","notation":["91A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Utility theory for games"},"scopeNote":{"en":["See also 91B16"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A35","notation":["91A35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Decision theory for games"},"scopeNote":{"en":["See also 62Cxx, 90B50, 91B06"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A40","notation":["91A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other game-theoretic models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A43","notation":["91A43"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Games involving graphs"},"scopeNote":{"en":["For games on graphs, see 05C57"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A44","notation":["91A44"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Games involving topology, set theory, or logic"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A46","notation":["91A46"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial games"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A50","notation":["91A50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Discrete-time games"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A55","notation":["91A55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Games of timing"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A60","notation":["91A60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Probabilistic games; gambling"},"scopeNote":{"en":["See also 60G40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A65","notation":["91A65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Hierarchical games (including Stackelberg games)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A68","notation":["91A68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Algorithmic game theory and complexity"},"scopeNote":{"en":["See also 68Qxx, 68Wxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A70","notation":["91A70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spaces of games"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A80","notation":["91A80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of game theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A81","notation":["91A81"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Quantum games"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A86","notation":["91A86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Game theory and fuzziness"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A90","notation":["91A90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Experimental studies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91A99","notation":["91A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Axx","notation":["91Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical economics"},"scopeNote":{"en":["For econometrics, see 62P20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91-XX","notation":["91-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B02","notation":["91B02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fundamental topics (basic mathematics, methodology; applicable to economics in general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B03","notation":["91B03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mechanism design theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B05","notation":["91B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Risk models (general)"},"scopeNote":{"en":["For actuarial and financial risk, see 91Gxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B06","notation":["91B06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Decision theory"},"scopeNote":{"en":["See also 62Cxx, 90B50, 91A35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B08","notation":["91B08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Individual preferences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B10","notation":["91B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Group preferences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B12","notation":["91B12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Voting theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B14","notation":["91B14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Social choice"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B15","notation":["91B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Welfare economics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B16","notation":["91B16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Utility theory"},"scopeNote":{"en":["See also 91A30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B18","notation":["91B18"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Public goods"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B24","notation":["91B24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Microeconomic theory (price theory and economic markets)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B26","notation":["91B26"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Auctions, bargaining, bidding and selling, and other market models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B32","notation":["91B32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Resource and cost allocation (including fair division, apportionment, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B38","notation":["91B38"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Production theory, theory of the firm"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B39","notation":["91B39"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Labor markets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B41","notation":["91B41"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Contract theory (moral hazard, adverse selection)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B42","notation":["91B42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Consumer behavior, demand theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B43","notation":["91B43"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Principal-agent models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B44","notation":["91B44"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Economics of information"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B50","notation":["91B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General equilibrium theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B51","notation":["91B51"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Dynamic stochastic general equilibrium theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B52","notation":["91B52"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special types of economic equilibria"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B54","notation":["91B54"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Special types of economic markets (including Cournot, Bertrand)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B55","notation":["91B55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Economic dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B60","notation":["91B60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Trade models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B62","notation":["91B62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Economic growth models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B64","notation":["91B64"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Macroeconomic theory (monetary models, models of taxation)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B66","notation":["91B66"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Multisectoral models in economics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B68","notation":["91B68"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Matching models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B69","notation":["91B69"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Heterogeneous agent models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B70","notation":["91B70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic models in economics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B72","notation":["91B72"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spatial models in economics"},"scopeNote":{"en":["See also 91D25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B74","notation":["91B74"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Economic models of real-world systems (e.g., electricity markets, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B76","notation":["91B76"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Environmental economics (natural resource models, harvesting, pollution, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B80","notation":["91B80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of statistical and quantum mechanics to economics (econophysics)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B82","notation":["91B82"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical methods; economic indices and measures"},"scopeNote":{"en":["See also 62P20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B84","notation":["91B84"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Economic time series analysis"},"scopeNote":{"en":["For statistical theory of time series, see 62M10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B86","notation":["91B86"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical economics and fuzziness"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91B99","notation":["91B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Bxx","notation":["91Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91Cxx","notation":["91Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Social and behavioral sciences: general topics"},"scopeNote":{"en":["For statistics, see 62P25"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91-XX","notation":["91-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91C05","notation":["91C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measurement theory in the social and behavioral sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Cxx","notation":["91Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91C15","notation":["91C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"One- and multidimensional scaling in the social and behavioral sciences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Cxx","notation":["91Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91C20","notation":["91C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Clustering in the social and behavioral sciences"},"scopeNote":{"en":["See also 62H30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Cxx","notation":["91Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91C99","notation":["91C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Cxx","notation":["91Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91Dxx","notation":["91Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical sociology (including anthropology)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91-XX","notation":["91-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91D10","notation":["91D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Models of societies, social and urban evolution"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Dxx","notation":["91Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91D15","notation":["91D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Social learning"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Dxx","notation":["91Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91D20","notation":["91D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical geography and demography"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Dxx","notation":["91Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91D25","notation":["91D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Spatial models in sociology"},"scopeNote":{"en":["See also 91B72"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Dxx","notation":["91Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91D30","notation":["91D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Social networks; opinion dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Dxx","notation":["91Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91D35","notation":["91D35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Manpower systems in sociology"},"scopeNote":{"en":["See also 90B70, 91B39"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Dxx","notation":["91Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91D99","notation":["91D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Dxx","notation":["91Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91Exx","notation":["91Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical psychology"},"scopeNote":{"en":["For psychometrics, see 62P15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91-XX","notation":["91-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91E10","notation":["91E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cognitive psychology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Exx","notation":["91Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91E30","notation":["91E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Psychophysics and psychophysiology; perception"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Exx","notation":["91Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91E40","notation":["91E40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Memory and learning in psychology"},"scopeNote":{"en":["See also 68T05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Exx","notation":["91Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91E45","notation":["91E45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measurement and performance in psychology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Exx","notation":["91Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91E99","notation":["91E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Exx","notation":["91Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91Fxx","notation":["91Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other social and behavioral sciences (mathematical treatment)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91-XX","notation":["91-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91F10","notation":["91F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History, political science"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Fxx","notation":["91Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91F20","notation":["91F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Linguistics"},"scopeNote":{"en":["See also 03B65, 68T50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Fxx","notation":["91Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91F99","notation":["91F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Fxx","notation":["91Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Actuarial science and mathematical finance"},"scopeNote":{"en":["For statistics, see 62P05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91-XX","notation":["91-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91G05","notation":["91G05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Actuarial mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91G10","notation":["91G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Portfolio theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91G15","notation":["91G15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Financial markets"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91G20","notation":["91G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Derivative securities (option pricing, hedging, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91G30","notation":["91G30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Interest rates, asset pricing, etc. (stochastic models)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91G40","notation":["91G40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Credit risk"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91G45","notation":["91G45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Financial networks (including contagion, systemic risk, regulation)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91G50","notation":["91G50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Corporate finance (dividends, real options, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91G60","notation":["91G60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Numerical methods (including Monte Carlo methods)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91G70","notation":["91G70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Statistical methods; risk measures"},"scopeNote":{"en":["See also 62P05, 62P20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91G80","notation":["91G80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Financial applications of other theories"},"scopeNote":{"en":["See also 35Q91, 37N40, 49N90, 60J70, 60K10, 60H30, 93E20"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/91G99","notation":["91G99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/91Gxx","notation":["91Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biology and other natural sciences"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/92-01","notation":["92-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92-02","notation":["92-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92-03","notation":["92-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of biology"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92-04","notation":["92-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92-05","notation":["92-05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Experimental work for problems pertaining to biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92-06","notation":["92-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92-08","notation":["92-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92-10","notation":["92-10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical modeling or simulation for problems pertaining to biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92-11","notation":["92-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92Bxx","notation":["92Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematical biology in general"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92B05","notation":["92B05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General biology and biomathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Bxx","notation":["92Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92B10","notation":["92B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Taxonomy, cladistics, statistics in mathematical biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Bxx","notation":["92Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92B15","notation":["92B15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General biostatistics"},"scopeNote":{"en":["See also 62P10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Bxx","notation":["92Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92B20","notation":["92B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Neural networks for/in biological studies, artificial life and related topics"},"scopeNote":{"en":["See also 68T05, 82C32, 94Cxx"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Bxx","notation":["92Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92B25","notation":["92B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biological rhythms and synchronization"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Bxx","notation":["92Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92B99","notation":["92B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Bxx","notation":["92Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Physiological, cellular and medical topics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C05","notation":["92C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biophysics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C10","notation":["92C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biomechanics"},"scopeNote":{"en":["See also 74L15"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C15","notation":["92C15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Developmental biology, pattern formation"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C17","notation":["92C17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cell movement (chemotaxis, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C20","notation":["92C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Neural biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C30","notation":["92C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Physiology (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C32","notation":["92C32"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pathology, pathophysiology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C35","notation":["92C35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Physiological flow"},"scopeNote":{"en":["See also 76Z05"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C37","notation":["92C37"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cell biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/92C42","notation":["92C42"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Systems biology, networks"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C45","notation":["92C45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)"},"scopeNote":{"en":["See also 80A30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C47","notation":["92C47"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biosensors (not for medical applications)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C50","notation":["92C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Medical applications (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C55","notation":["92C55"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biomedical imaging and signal processing"},"scopeNote":{"en":["See also 44A12, 65R10, 94A08, 94A12"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C60","notation":["92C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Medical epidemiology"},"scopeNote":{"en":["For theoretical aspects, see 92D30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C70","notation":["92C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Microbiology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C75","notation":["92C75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Biotechnology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C80","notation":["92C80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Plant biology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92C99","notation":["92C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Cxx","notation":["92Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92Dxx","notation":["92Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Genetics and population dynamics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92D10","notation":["92D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Genetics and epigenetics"},"scopeNote":{"en":["For genetic algebras, see 17D92"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Dxx","notation":["92Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92D15","notation":["92D15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Problems related to evolution"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Dxx","notation":["92Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92D20","notation":["92D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Protein sequences, DNA sequences"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Dxx","notation":["92Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92D25","notation":["92D25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Population dynamics (general)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Dxx","notation":["92Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92D30","notation":["92D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Epidemiology"},"scopeNote":{"en":["For medical applications, see 92C60"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Dxx","notation":["92Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92D40","notation":["92D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Ecology"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Dxx","notation":["92Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92D45","notation":["92D45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pest management"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Dxx","notation":["92Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92D50","notation":["92D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Animal behavior"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Dxx","notation":["92Dxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/92Exx","notation":["92Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Chemistry"},"scopeNote":{"en":["For biochemistry, see 92C40"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92E10","notation":["92E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Molecular structure (graph-theoretic methods, methods of differential topology, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Exx","notation":["92Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92E20","notation":["92E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Classical flows, reactions, etc. in chemistry"},"scopeNote":{"en":["See also 80A30, 80A32"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Exx","notation":["92Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92E99","notation":["92E99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Exx","notation":["92Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92Fxx","notation":["92Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other natural sciences (mathematical treatment)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92-XX","notation":["92-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92F05","notation":["92F05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other natural sciences (mathematical treatment)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Fxx","notation":["92Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/92F99","notation":["92F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/92Fxx","notation":["92Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/93-XX","notation":["93-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Systems theory; control"},"scopeNote":{"en":["For optimal control, see 49-XX"]},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/93-00","notation":["93-00"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to systems and control theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/93-XX","notation":["93-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/93-01","notation":["93-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/93-XX","notation":["93-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/93-02","notation":["93-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to systems and control theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/93-XX","notation":["93-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/93-03","notation":["93-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of systems and control theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/93-XX","notation":["93-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/93D30","notation":["93D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Lyapunov and storage functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/93Dxx","notation":["93Dxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/93D50","notation":["93D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Consensus"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/93Dxx","notation":["93Dxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/93E11","notation":["93E11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Filtering in stochastic control theory"},"scopeNote":{"en":["See also 60G35"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/93Exx","notation":["93Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/93E12","notation":["93E12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Identification in stochastic control theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/93Exx","notation":["93Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/93E14","notation":["93E14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Data smoothing in stochastic control theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/93Exx","notation":["93Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/93E15","notation":["93E15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Stochastic stability in control theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/93Exx","notation":["93Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/93E20","notation":["93E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Optimal stochastic control"},"scopeNote":{"en":["See also 49J55, 49K45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/93Exx","notation":["93Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/93E24","notation":["93E24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Least squares and related methods for stochastic control systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/93Exx","notation":["93Exx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/94-01","notation":["94-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94-XX","notation":["94-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94-02","notation":["94-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to information and communication theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94-XX","notation":["94-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94-03","notation":["94-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of information and communication theory"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94-XX","notation":["94-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94-04","notation":["94-04"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Software, source code, etc. for problems pertaining to information and communication theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94-XX","notation":["94-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94-05","notation":["94-05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Experimental work for problems pertaining to information and communication theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94-XX","notation":["94-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94-06","notation":["94-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to information and communication theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94-XX","notation":["94-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94-08","notation":["94-08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Computational methods for problems pertaining to information and communication theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94-XX","notation":["94-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/94A05","notation":["94A05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Communication theory"},"scopeNote":{"en":["See also 60G35, 90B18"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94A08","notation":["94A08"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Image processing (compression, reconstruction, etc.) in information and communication theory"},"scopeNote":{"en":["See also 68U10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94A11","notation":["94A11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Application of orthogonal and other special functions"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94A12","notation":["94A12"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Signal theory (characterization, reconstruction, filtering, etc.)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94A13","notation":["94A13"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Detection theory in information and communication theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94A14","notation":["94A14"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Modulation and demodulation in information and communication theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94A15","notation":["94A15"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Information theory (general)"},"scopeNote":{"en":["See also 62B10, 81P45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94A16","notation":["94A16"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Informational aspects of data analysis and big data"},"scopeNote":{"en":["See also 62R07, 68T09; For homological aspects, see 55N31"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94A17","notation":["94A17"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Measures of information, entropy"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94A20","notation":["94A20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sampling theory in information and communication theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94A24","notation":["94A24"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Coding theorems (Shannon theory)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94A29","notation":["94A29"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Source coding"},"scopeNote":{"en":["See also 68P30"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94A34","notation":["94A34"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Rate-distortion theory in information and communication theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/94A45","notation":["94A45"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Prefix, length-variable, comma-free codes"},"scopeNote":{"en":["See also 20M35, 68Q45"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/94A62","notation":["94A62"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Authentication, digital signatures and secret sharing"},"scopeNote":{"en":["See also 81P94"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Axx","notation":["94Axx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/94Bxx","notation":["94Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Theory of error-correcting codes and error-detecting codes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94-XX","notation":["94-XX"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/94B25","notation":["94B25"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Combinatorial codes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Bxx","notation":["94Bxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/94B30","notation":["94B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Majority codes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Bxx","notation":["94Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94B35","notation":["94B35"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Decoding"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Bxx","notation":["94Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94B40","notation":["94B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Arithmetic codes"},"scopeNote":{"en":["See also 11T71, 14G50"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Bxx","notation":["94Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94B50","notation":["94B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Synchronization error-correcting codes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Bxx","notation":["94Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94B60","notation":["94B60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Other types of codes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Bxx","notation":["94Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94B65","notation":["94B65"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Bounds on codes"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Bxx","notation":["94Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94B70","notation":["94B70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Error probability in coding theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Bxx","notation":["94Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94B75","notation":["94B75"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory"},"scopeNote":{"en":["See also 11H31, 11H71"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Bxx","notation":["94Bxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/94C05","notation":["94C05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytic circuit theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Cxx","notation":["94Cxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/94C60","notation":["94C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Circuits in qualitative investigation and simulation of models"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Cxx","notation":["94Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94C99","notation":["94C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Cxx","notation":["94Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94Dxx","notation":["94Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Miscellaneous topics in information and communication theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94-XX","notation":["94-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94D05","notation":["94D05"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Fuzzy sets and logic (in connection with information, communication, or circuits theory)"},"scopeNote":{"en":["See also 03B52, 03E72, 28E10"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Dxx","notation":["94Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94D10","notation":["94D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Boolean functions"},"scopeNote":{"en":["See also 06E30; For connections with circuits and networks, see 94C11"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Dxx","notation":["94Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/94D99","notation":["94D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/94Dxx","notation":["94Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematics education"},"topConceptOf":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/97-01","notation":["97-01"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97-02","notation":["97-02"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research exposition (monographs, survey articles) pertaining to mathematics education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97-03","notation":["97-03"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History of mathematics education"},"scopeNote":{"en":["Consider also classification numbers pertaining to Section 01"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97-06","notation":["97-06"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Proceedings, conferences, collections, etc. pertaining to mathematics education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97-11","notation":["97-11"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Research data for problems pertaining to mathematics education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97Axx","notation":["97Axx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History and society (aspects of mathematics education)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97A30","notation":["97A30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"History in mathematics education"},"scopeNote":{"en":["For mathematics history, see 01-XX; for biographies, see 01A70; for history of mathematics education, see 97-03"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Axx","notation":["97Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97A40","notation":["97A40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematics education and society"},"scopeNote":{"en":["For sociology (and profession) of mathematics, see 01A80"]},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Axx","notation":["97Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97A99","notation":["97A99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Axx","notation":["97Axx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97Bxx","notation":["97Bxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Educational policy and systems"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97B10","notation":["97B10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematics educational research and planning"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Bxx","notation":["97Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97B20","notation":["97B20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Educational policy for general education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Bxx","notation":["97Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97B30","notation":["97B30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Educational policy for vocational education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Bxx","notation":["97Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97B40","notation":["97B40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Educational policy for higher education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Bxx","notation":["97Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97B50","notation":["97B50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematics teacher education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Bxx","notation":["97Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97B60","notation":["97B60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Educational policy for adult and further education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Bxx","notation":["97Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97B70","notation":["97B70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Syllabuses, educational standards"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Bxx","notation":["97Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97B99","notation":["97B99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Bxx","notation":["97Bxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97Cxx","notation":["97Cxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Psychology of mathematics education, research in mathematics education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97C10","notation":["97C10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Comprehensive works on psychology of mathematics education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Cxx","notation":["97Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97C20","notation":["97C20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Affective behavior and mathematics education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Cxx","notation":["97Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97C30","notation":["97C30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Cognitive processes, learning theories (aspects of mathematics education)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Cxx","notation":["97Cxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/97C50","notation":["97C50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Language and verbal communities (aspects of mathematics education)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Cxx","notation":["97Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97C60","notation":["97C60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Sociological aspects of learning (aspects of mathematics education)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Cxx","notation":["97Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97C70","notation":["97C70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Teaching-learning processes in mathematics education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Cxx","notation":["97Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97C99","notation":["97C99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Cxx","notation":["97Cxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97Dxx","notation":["97Dxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Education and instruction in mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97D10","notation":["97D10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Comprehensive works and comparative studies on education and instruction in mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Dxx","notation":["97Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97D20","notation":["97D20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Philosophical and theoretical contributions (maths didactics)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Dxx","notation":["97Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97D30","notation":["97D30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Objectives and goals of mathematics teaching"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Dxx","notation":["97Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97D40","notation":["97D40"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematics teaching methods and classroom techniques"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Dxx","notation":["97Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97D50","notation":["97D50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Teaching mathematical problem solving and heuristic strategies"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Dxx","notation":["97Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97D60","notation":["97D60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Student assessment, achievement control and rating (aspects of mathematics education)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Dxx","notation":["97Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97D70","notation":["97D70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Learning difficulties and student errors (aspects of mathematics education)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Dxx","notation":["97Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97D80","notation":["97D80"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Mathematics teaching units and draft lessons"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Dxx","notation":["97Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97D99","notation":["97D99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Dxx","notation":["97Dxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97Exx","notation":["97Exx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Education of foundations of mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97E10","notation":["97E10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Comprehensive works on education of foundations of mathematics"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Exx","notation":["97Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97E20","notation":["97E20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Philosophy and mathematics (educational aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Exx","notation":["97Exx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97E30","notation":["97E30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Logic (educational aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Exx","notation":["97Exx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/97Fxx","notation":["97Fxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Education of arithmetic and number theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97F10","notation":["97F10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Comprehensive works on education of arithmetic and number theory"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Fxx","notation":["97Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97F20","notation":["97F20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Pre-numerical stage, concept of numbers"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Fxx","notation":["97Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97F30","notation":["97F30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Natural numbers (educational aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Fxx","notation":["97Fxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/97F90","notation":["97F90"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Real life mathematics, practical arithmetic (educational aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Fxx","notation":["97Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97F99","notation":["97F99"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"None of the above, but in this section"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Fxx","notation":["97Fxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97Gxx","notation":["97Gxx"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Geometry education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97-XX","notation":["97-XX"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97G10","notation":["97G10"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Comprehensive works on geometry education"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Gxx","notation":["97Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97G20","notation":["97G20"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Informal geometry (educational aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Gxx","notation":["97Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97G30","notation":["97G30"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Area and volume (educational aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Gxx","notation":["97Gxx"]}]}
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{"uri":"http://uri.gbv.de/terminology/msc2020/97G50","notation":["97G50"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Transformation geometry (educational aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Gxx","notation":["97Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97G60","notation":["97G60"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Plane and spherical trigonometry (educational aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Gxx","notation":["97Gxx"]}]}
{"uri":"http://uri.gbv.de/terminology/msc2020/97G70","notation":["97G70"],"inScheme":[{"uri":"http://uri.gbv.de/terminology/msc2020/"}],"prefLabel":{"en":"Analytic geometry, vector algebra (educational aspects)"},"broader":[{"uri":"http://uri.gbv.de/terminology/msc2020/97Gxx","notation":["97Gxx"]}]}
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