# Connected component of a 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)



## [Connected component of a topological space](https://ocme.evemisslab.com/en/atlas/atlas-topological-connected-component/)

The component of a point is its unique inclusion-maximal connected subset; components partition the space and are closed.

atlas-topological-connected-component · canonical_mko

[Connected component of a topological space](https://ocme.evemisslab.com/en/mko/mko-topological-connected-component/)

## Prerequisite nodes


- [Connected topological space](https://ocme.evemisslab.com/en/atlas/atlas-connected-topological-space/)
- [Equivalence class](https://ocme.evemisslab.com/en/atlas/atlas-equivalence-class/)
- [Subset](https://ocme.evemisslab.com/en/atlas/atlas-subset/)
- [Topological closure and interior](https://ocme.evemisslab.com/en/atlas/atlas-closure-and-interior/)
- [Connected component](https://ocme.evemisslab.com/en/atlas/atlas-connected-component/)
- [Subspace topology](https://ocme.evemisslab.com/en/atlas/atlas-subspace-topology/)