# Definition:Interior (Topology)/Definition 3

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## Definition

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

Let $H \subseteq S$.

The **interior** of $H$ is the set of all interior points of $H$.

## 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.

## Also see

## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**interior of a set**