Definition:Open Neighborhood/Topology

Definition

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

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

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

If $N_A \in \tau$, i.e. if $N_A$ is itself open in $T$, then $N_A$ is called an open neighborhood.