Definition:Neighborhood (Complex Analysis)

Definition

Let $z_0 \in \C$ be a complex number.

Let $\epsilon \in \R: \epsilon > 0$ be a positive real number.

The $\epsilon$-neighborhood of $z_0$ is defined as:

$N_\epsilon \left({z_0}\right) := \left\{{z \in \C: \left|{z - z_0}\right| < \epsilon}\right\}$

In this context, a neighborhood is often referred to as an open disk (UK spelling: open disc).

Linguistic Note

The UK English spelling of this is neighbourhood.