\begin{definition}[Definition:Boundary (Topology)/Definition 3]
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$.
The '''boundary of $H$''' is the intersection of the closure of $H$ with the closure of the complement of $H$ in $T$:
:$\partial H = H^- \cap \paren {\overline H}^-$
\end{definition}