\begin{definition}[Definition:Neighborhood Sub-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 sub-basis of $x$ relative to $\tau$''' {{iff}}:
:for each neighborhood $N$ of $x$, there exists a finite subset $K$ of $\BB$ such that $\bigcap K \subseteq N$.
\end{definition}