# Definition:Interior (Topology)/Notation

Jump to navigation
Jump to search

## Definition

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

Let $H \subseteq S$.

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.

## Sources

- 2013: Francis Clarke:
*Functional Analysis, Calculus of Variations and Optimal Control*... (previous) ... (next): $1.1$: Basic Definitions