Definition of a Riemann Sphere
Definition 1
The Riemann Sphere refers to the two-dimensional unit sphere, $2$-sphere $S^{2} \subset \mathbb{R}^{3}$, that is homeomorphic to the extended complex plane $\overline{\mathbb{C}} = \mathbb{C} \cup \left\{ \infty \right\}$ through one-point compactification. $$ \widetilde{\mathbb{C}} := S^{2} \simeq \overline{\mathbb{C}} $$
Osborne (1999). Complex variables and their applications: p13. ↩︎