📂Complex Anaylsis

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. $$\widetilde{\mathbb{C}} := S^{2} \simeq \overline{\mathbb{C}}$$