Definition:Interior (Topology)

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $H \subseteq S$.

Equivalence of Definitions
The equivalence of these definitions is demonstrated in Set Interior is Largest Open Set.

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.

Also see

 * Closure