\begin{definition}[Definition:Neighborhood Basis]
Let $\struct {S, \tau}$ be a topological space.
Let $x \in S$.
Let $\BB$ be a set of neighborhoods of $x$.
Then $\BB$ is a '''neighborhood basis''' at $x$ {{iff}}:
:For each neighborhood $N$ of $x$, there is an $M \in \BB$ such that $M \subseteq N$.
\end{definition}