\begin{definition}[Definition:Boundary (Topology)/Definition 2]
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$.
$x \in S$ is a '''boundary point''' of $H$ if every neighborhood $N$ of $x$ satisfies:
:$H \cap N \ne \O$
and
:$\overline H \cap N \ne \O$
where $\overline H$ is the complement of $H$ in $S$.
The '''boundary of $H$''' consists of all the '''boundary points''' of $H$.
\end{definition}