Definition:Open Neighborhood

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

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

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

Let:
 * $N_A \in \tau$

That is, let $N_A$ itself be an open set of $T$.

Then $N_A$ is called an open neighborhood of $A$ in $T$.

Also see

 * Set is Open iff Neighborhood of all its Points
 * Open Superset is Open Neighborhood: $N_A$ is an open neighborhood of $A$ $N_A$ is an open set in $T$ such that $A \subseteq N_A$.