Definition:Neighborhood Basis

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

Let $x \in X$ be a point in $X$.

A neighborhood basis (or local basis) for $x$ is a countable set $\mathcal V$ of open neighborhoods of $x$ such that each open set of $X$ containing $x$ also contains an element of $\mathcal V$.