\begin{definition}[Definition:Isolated Singularity]
Let $U$ be an open subset of a Riemann surface.
Let $z_0 \in U$.
Let $f: U \setminus \left\{{z_0}\right\} \to \C$ be a holomorphic function.
Then $f$ has an '''isolated singularity''' at $z_0$.
In most applications, the Riemann surface in question is the complex plane or the Riemann sphere.
{{refactor|Move the following into a parallel definition page, transcluded appropriately.}}
(Equivalently, an isolated singularity is an isolated point of the complement of the domain of definition of $f$.)
\end{definition}