Category:Definitions/Isolated Singularities

This category contains definitions related to Isolated Singularities.
Related results can be found in Category:Isolated Singularities.

Complex Function

Let $U \subseteq \C$ be an open set.

Let $f : U \to \C$ be a holomorphic function.

An isolated singularity of $f$ is a point $z_0 \in \C$ for which $U$ is a punctured neighborhood.

Riemann Surface

Let $U$ be an open set of a Riemann surface.

Let $z_0 \in U$.

Let $f: U \setminus \set {z_0} \to \C$ be a holomorphic function.

Then $f$ has an isolated singularity at $z_0$.