Definition:Isolated Singularity/Riemann Surface

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Definition

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 $z_0$.

In most applications, the Riemann surface in question is the complex plane or the Riemann sphere.

Also see

• Results about isolated singularities can be found here.