For questions about the Riemann sphere, a model of the extended complex plane.
The set of extended complex numbers, or Riemann sphere, consists of the set $\mathbb{C}$ of complex numbers, together with a point $\infty$. This can be viewed as a sphere via stereographic projection from the north pole, with the pole itself identified with $\infty$.
From a topological viewpoint, the Riemann sphere is a one-point compactification of the space $\mathbb{C}$. In fact, the sphere can be viewed as a complex manifold with a well-defined complex structure.
It is known that the automorphisms of the Riemann sphere are precisely the Mobius transformations.
Reference: Riemann sphere.
