# Homeomorphism

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)



## [Homeomorphism](https://ocme.evemisslab.com/en/atlas/atlas-homeomorphism/)

A homeomorphism is a bijection that is continuous in both directions; a continuous bijection alone need not be a homeomorphism.

atlas-homeomorphism · canonical_mko

[Homeomorphism](https://ocme.evemisslab.com/en/mko/mko-homeomorphism/)

## Prerequisite nodes


- [Continuous maps between topological spaces](https://ocme.evemisslab.com/en/atlas/atlas-topological-continuity/)
- [Bijectivity and unique preimages](https://ocme.evemisslab.com/en/atlas/atlas-bijective/)
- [Inverse functions of bijections](https://ocme.evemisslab.com/en/atlas/atlas-inverse-function/)
- [Topological space](https://ocme.evemisslab.com/en/atlas/atlas-topological-space/)