# Neighborhood

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)



## [Neighborhood](https://ocme.evemisslab.com/en/atlas/atlas-neighborhood/)

A set N is a neighborhood of x exactly when N contains an open set containing x; N itself need not be open.

atlas-neighborhood · canonical_mko

[Neighborhood](https://ocme.evemisslab.com/en/mko/mko-neighborhood/)

## Prerequisite nodes


- [Topological space](https://ocme.evemisslab.com/en/atlas/atlas-topological-space/)
- [Open and closed sets](https://ocme.evemisslab.com/en/atlas/atlas-open-closed-set/)
- [Set membership](https://ocme.evemisslab.com/en/atlas/atlas-set-membership/)