Definition:Interior Point (Topology)
Jump to navigation
Jump to search
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 $H$.