---
tag: 0NA0732YAG
kind: concept
name: Basis of a topology
aliases: [base-of-a-topology, topological-basis]
msc: [54A05]
sources:
  - url: https://en.wikipedia.org/wiki/Base_(topology)
    locator: lead section
same_as:
  wikidata: Q810214
  wikipedia: Base (topology)
---

## Summary

A basis of a topology is a family of open sets such that every open set is a union of members of the family.
A basis lets you describe a topology by a small set of simple open sets, such as open intervals or open balls.