---
tag: 0QEAJB91GZ
kind: concept
name: Closure
aliases: [closure-of-a-set]
msc: [54A05]
sources:
  - url: https://en.wikipedia.org/wiki/Closure_(topology)
    locator: lead section
same_as:
  wikidata: Q320346
  wikipedia: Closure (topology)
---

## Summary

The closure of a subset of a topological space is the intersection of all closed sets that contain it.
It is the smallest closed set that contains the subset.
In a metric space, it is the set of limits of convergent sequences of points of the subset.