# Definition:Interior Point (Topology)

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*This page is about interior points in the context of topology. For other uses, see Definition:Interior Point.*

## Definition

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

Let $H \subseteq S$.

### Definition 1

Let $h \in H$.

Then $h$ is an **interior point** of $H$ iff:

- $h \in H^\circ$

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

### Definition 2

Let $h \in H$.

$h$ is an **interior point** of $H$ iff $h$ has an open neighborhood $N_h$ such that $N_h \subseteq H$.