Definition:Interior Point (Topology)

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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 $H$.


Also see