Definition:Interior (Topology)/Definition 1

Definition
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:
 * $\displaystyle H^\circ := \bigcup_{K \mathop \in \mathbb K} K$

where $\mathbb K = \set {K \in \tau: K \subseteq H}$.

Also see

 * Equivalence of Definitions of Interior (Topology)