Definition:Isolated Zero

Definition

Let $f: \C \to \C$ be a complex function.

Let $\map f {z_0} = 0$ for some $z_0 \in \C$.

We say $z_0$ is an isolated zero of $f$ if and only if there exists an open ball $B$ containing $z_0$, such that $\map f w \ne 0$ for all $w \in B \setminus \set {z_0}$.