# Quotient topology

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)



## [Quotient topology](https://ocme.evemisslab.com/en/atlas/atlas-quotient-topology/)

For a surjection q:X→Y, the quotient topology declares U open exactly when its full preimage under q is open.

atlas-quotient-topology · canonical_mko

[Quotient topology](https://ocme.evemisslab.com/en/mko/mko-quotient-topology/)

## Prerequisite nodes


- [Topological space](https://ocme.evemisslab.com/en/atlas/atlas-topological-space/)
- [Quotient set](https://ocme.evemisslab.com/en/atlas/atlas-quotient-set/)
- [Surjectivity and codomain coverage](https://ocme.evemisslab.com/en/atlas/atlas-surjective/)
- [Continuous maps between topological spaces](https://ocme.evemisslab.com/en/atlas/atlas-topological-continuity/)
- [Function composition](https://ocme.evemisslab.com/en/atlas/atlas-composition/)