---
tag: 0GWN3CMRK8
kind: concept
name: One-point compactification
aliases: [alexandroff-extension, alexandroff-compactification]
msc: [54D35]
sources:
  - url: https://en.wikipedia.org/wiki/Alexandroff_extension
    locator: lead section
same_as:
  wikidata: Q864919
  wikipedia: Alexandroff extension
---

## Summary

The one-point compactification of a topological space adds one point at infinity and makes the space compact.
For example, the plane with one added point is the sphere.