\begin{definition}[Definition:Boundary (Topology)/Definition 1]
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$.
The '''boundary of $H$''' consists of all the points in the closure of $H$ which are not in the interior of $H$.
Thus, the '''boundary of $H$''' is defined as:
:$\partial H := H^- \setminus H^\circ$
where $H^-$ denotes the closure and $H^\circ$ the interior of $H$.
\end{definition}