Definition:Neighborhood Sub-Basis

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

Let $x \in S$.

Let $\mathcal B$ be a set of neighborhoods of $x$.

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

Also see

 * Definition:Neighborhood Basis
 * Definition:Local Sub-Basis