Definition:Neighborhood (Topology)/Point

Definition
Let $T = \left({X, \tau}\right)$ be a topological space. Let $z \in X$ be a point in a $X$.

A neighborhood of $z$, which can be denoted $N_z$, is any subset of $X$ containing an open set of $T$ which itself contains $z$.

That is:
 * $\exists U \in \tau: z \in U \subseteq N_z \subseteq X$

Linguistic Note
The UK English spelling of this is neighbourhood.