# Compact topological space

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Compact topological space](https://ocme.evemisslab.com/en/atlas/atlas-compact-topological-space/)

A space is compact when every open cover has a finite subcover; every finite topological space is compact.

atlas-compact-topological-space · canonical_mko

[Compact topological space](https://ocme.evemisslab.com/en/mko/mko-compact-topological-space/)

## Prerequisite nodes


- [Topological space](https://ocme.evemisslab.com/en/atlas/atlas-topological-space/)
- [Open cover and subcover](https://ocme.evemisslab.com/en/atlas/atlas-open-cover-and-subcover/)
- [Quantifiers and explicit domains](https://ocme.evemisslab.com/en/atlas/atlas-quantifier/)