---
tag: 0R6EWFKRCF
kind: concept
name: Compact set
aliases: [compact-subset]
msc: [54D30]
sources:
  - url: https://en.wikipedia.org/wiki/Compact_space
    locator: Compactness of subsets
---

## Summary

A compact subset of a topological space is a subset that is a compact space with the subspace topology.
Equivalently, each cover of the subset by open sets of the space has a finite subcover.