---
tag: 0FRMJH3CY7
kind: concept
name: Sequential compactness
aliases: [sequentially-compact-space, sequentially-compact-set]
msc: [54D30]
sources:
  - url: https://en.wikipedia.org/wiki/Sequentially_compact_space
    locator: lead section
same_as:
  wikidata: Q1135427
  wikipedia: Sequentially compact space
---

## Summary

A space or a set is sequentially compact when each sequence in it has a subsequence that converges to a point of it.
In metric spaces, sequential compactness is the same as compactness.