Definition:Isolated Singularity/Complex Function

Definition

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.

Also see

• Results about isolated singularities can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): isolated singularity
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): singular point (singularity): 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): isolated singularity
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): singular point (singularity): 1.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): isolated singularity