# A compact subset of a Hausdorff space is closed

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)



## [A compact subset of a Hausdorff space is closed](https://ocme.evemisslab.com/en/atlas/atlas-compact-subset-closed-in-hausdorff/)

If K is compact in the Hausdorff space X, then K is closed in X.

atlas-compact-subset-closed-in-hausdorff · canonical_mko

[A compact subset of a Hausdorff space is closed](https://ocme.evemisslab.com/en/mko/mko-compact-subset-closed-in-hausdorff/)

## Prerequisite nodes


- [Hausdorff space](https://ocme.evemisslab.com/en/atlas/atlas-hausdorff-space/)
- [Compact subset](https://ocme.evemisslab.com/en/atlas/atlas-compact-subset/)
- [Open and closed sets](https://ocme.evemisslab.com/en/atlas/atlas-open-closed-set/)