Definition:Interior (Topology)/Definition 2

Definition
Let $T = \left({S, \tau}\right)$ 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 $H$.

This fact is demonstrated in Set Interior is Largest Open Set.

Interior Point
An interior point of $H$ is any point in the interior of $H$.

Notation
The interior of $H$ can be denoted:
 * $\operatorname{Int} \left({H}\right)$
 * $H^\circ$

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 this website, $H^\circ$ is the notation of choice.