\begin{definition}[Definition:Boundary Point (Complex Analysis)]
Let $S \subseteq \C$ be a subset of the complex plane.
Let $z_0 \in \C$.
$z_0$ is a '''boundary point''' of $S$ {{iff}} every $\epsilon$-neighborhood $\map {N_\epsilon} {z_0}$ of $z_0$ contains points of $\C$ in $S$ and also points of $\C$ which are not in $S$.
\end{definition}