# Definition:Neighborhood Sub-Basis

Jump to navigation Jump to search

## 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 $\bigcap K \subseteq N$.