---
tag: 0ZH5AJ2ED7
kind: concept
name: Baire space
msc: ["54E52"]
sources:
  - url: https://en.wikipedia.org/wiki/Baire_space
    locator: lead section
same_as:
  wikidata: Q1150180
  wikipedia: Baire space
---

## Summary

A Baire space is a topological space in which countable unions of closed sets with empty interior have empty interior.
Equivalently, countable intersections of dense open sets are dense.