# Topological Space is Open Neighborhood of Subset

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## Theorem

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

Let $H \subseteq S$ be a subset of $S$.

Then $S$ is an open neighborhood of $H$.

## Proof

From Underlying Set of Topological Space is Clopen, $S$ is open in $T$.

By hypothesis, $H \subseteq S$.

The result follows from Open Superset is Open Neighborhood.

$\blacksquare$