---
layout: default
title: “Elementary properties of closures”
comments: "yes"
disqus-id: 01645ab99bebdabf308d8cdc05eff0109abec049
math: "yes"
license: "CC-BY"
tags: math, analysis
---

From Terence Tao’s *Analysis I*, p213 of the hardcover second edition, Lemma 9.1.11.

Showing $X\subset \overline{X}$. Let $x\in X$, and let $\epsilon >0$. We have $\left|{x-x}\right| = 0 \leq \epsilon$, so we are done.