In mathematics, the

**Riemann sphere**of complex analysis is a compact Riemann surface, which consists of a complex plane and a point at infinity.

It can be represented by an atlas with two charts, and a transition function *z=1/w* where *w* and *z* are nonzero. Topologically, it is just a sphere.

The Riemann sphere can be conformally mapped onto a euclidian plane by stereographic projection.

See also: