Definition:Neighborhood Sub-Basis

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

Let $x \in X$.

Let $S$ be a set of neighborhoods of $x$.

Then $S$ is a neighborhood sub-basis of $x$ relative to $\tau$ iff for each neighborhood $N$ of $x$, there is a finite subset $K$ of $S$ such that:
 * $\bigcap K$ is a neighborhood of $x$.
 * $\bigcap K \subseteq N$.