Definition:Open Neighborhood/Point

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

Let $N_x$ be a neighborhood of $x$ in $T$.

Let:
 * $N_x \in \tau$

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

Then $N_x$ is called an open neighborhood of $x$ in $T$.