# Definition:Interior Point (Topology)

This page is about Interior Point in the context of topology. For other uses, see Interior Point.

## Definition

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

Let $H \subseteq S$.

### Definition 1

Let $h \in H$.

Then $h$ is an interior point of $H$ if and only if:

$h \in H^\circ$

where $H^\circ$ denotes the interior of $H$.

### Definition 2

Let $h \in H$.

$h$ is an interior point of $H$ if and only if $h$ has an open neighborhood $N_h$ such that $N_h \subseteq H$.

### Definition 3

Let $h \in H$.

$h$ is an interior point of $H$ if and only if $h$ is an element of an open set of the subspace topology of $H$.