Definition:Closed Neighborhood

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

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

Let $N_A$ be a neighborhood of $A$.

If $\relcomp S {N_A} \in \tau$, that is if $N_A$ is closed in $S$, then $N_A$ is called a closed neighborhood.

Linguistic Note

The UK English spelling of neighborhood is neighbourhood.