Added Runge's theorem.

src/dg/complex/sphere.tex

@@ -0,0 +1,16 @@
+\section{The Riemann Sphere}
+\label{section:riemann-sphere}
+
+
+\begin{definition}[Extended Complex Plane]
+\label{definition:extended-complex-plane}
+    Let $\complex$ be the complex plane, then its one-point compactification $\complex_\infty = \complex \sqcup \bracs{\infty}$ is the \textbf{extended complex plane}. 
+\end{definition}
+
+\begin{definition}[Holomorphic on $\complex_\infty$]
+\label{definition:holomorphic-on-sphere}
+    Let $E$ be a separated locally convex space and $f \in C(\complex_\infty; E)$, then $f$ is \textbf{holomorphic at $\infty$} if $z \mapsto f(z^{-1})$ (under the identification that $1/0 = \infty$) is holomorphic at $0$. 
+\end{definition}
+
+
+