# Compact subset

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 subset](https://ocme.evemisslab.com/en/atlas/atlas-compact-subset/)

A subset K of X is compact in its subspace topology exactly when every relative-open cover has a finite subcover.

atlas-compact-subset · canonical_mko

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

## Prerequisite nodes


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