Definition:Closed Neighborhood

Definition
Let $\left({X, \tau}\right)$ be a topological space.

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

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

If $\complement_X \left({N_A}\right) \in \tau$, that is if $N_A$ is closed in $X$, then $N_A$ is called a closed neighborhood.

Linguistic Note
The UK English spelling of this is neighbourhood.