\begin{definition}[Definition:Neighborhood (Complex Analysis)]
Let $z_0 \in \C$ be a complex number.
Let $\epsilon \in \R_{>0}$ be a (strictly) positive real number.
The '''$\epsilon$-neighborhood''' of $z_0$ is defined as:
:$\map {N_\epsilon} {z_0} := \set {z \in \C: \cmod {z - z_0} < \epsilon}$
\end{definition}