---
tag: 0J78KBPFZB
kind: concept
name: Riemann sphere
aliases: [extended-complex-plane, extended-complex-numbers]
msc: [30F10]
sources:
  - url: https://en.wikipedia.org/wiki/Riemann_sphere
    locator: lead section
same_as:
  wikidata: Q825857
  wikipedia: Riemann sphere
---

## Summary

The Riemann sphere is the complex plane with one added point $\infty$, see the [[definition|0CDMXGPSES]].
Stereographic projection identifies it with the unit sphere in $\mathbb{R}^3$.
It is the natural domain and target of [[Möbius transformations|0SG74WBFA2]] and of meromorphic functions.