---
tag: 00FSJTXPJM
kind: concept
name: Closed map
aliases: [closed-mapping]
msc: [54C10]
sources:
  - url: https://en.wikipedia.org/wiki/Open_and_closed_maps
    locator: lead section
---

## Summary

A closed map is a function between topological spaces that sends closed sets to closed sets.
Continuous maps from compact spaces to Hausdorff spaces are closed maps.