Definition:Neighborhood Sub-Basis

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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 $\bigcap K \subseteq N$.

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