# Definition:Interior (Topology)/Definition 2

## Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $H \subseteq S$.

The interior of $H$ is defined as the largest open set of $T$ which is contained in $H$.

## Notation

The interior of $H$ can be denoted:

$\map {\mathrm {Int} } H$
$H^\circ$

The first is regarded by some as cumbersome, but has the advantage of being clear.

$H^\circ$ is neat and compact, but has the disadvantage of being relatively obscure.

On $\mathsf{Pr} \infty \mathsf{fWiki}$, $H^\circ$ is the notation of choice.