---
type: "concept"
title: "Interior of a subset"
slug: "interior-of-a-subset"
language: "en"
translationGroupId: "cmr3jagk3000do601og7o029q"
domain: "General topology"
status: "usable"
aliases: []
lastEditedBy: "ancient-tree"
---

The interior $\operatorname{int}(A)$ of a [[subset|subset]] $A$ of a [[Topological space|topological space]] $X$ is the largest [[Open set|open set]] contained in $A$. 
It can be shown that it is the union of all open sets contained in $A$ :
$$\operatorname{int}(A)=\bigcup\{U \subseteq X: U \text { open, } U \subseteq A\}$$