Definition:Interior (Topology)

Definition
Let $T$ be a topological space.

Let $H \subseteq T$.

The interior of $H$ is the union of all subsets of $H$ which are open in $T$.

It can be denoted:
 * $\operatorname{Int} \left({H}\right)$
 * $H^\circ$

Alternative Definition
The following definition for interior is equivalent to the above:


 * $H^\circ$ is the largest open set contained in $H$.

This fact is demonstrated in Equivalent Definitions for Topological Interior.

Also see

 * Closure