\begin{definition}[Definition:Interior (Topology)/Definition 1]
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$.
The '''interior''' of $H$ is the union of all subsets of $H$ which are open in $T$.
That is, the '''interior''' of $H$ is defined as:
:$\ds H^\circ := \bigcup_{K \mathop \in \mathbb K} K$
where $\mathbb K = \set {K \in \tau: K \subseteq H}$.
\end{definition}