Definition:Interior (Topology)/Definition 2
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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.
Also see
- Results about set interiors can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Closures and Interiors