Definition:Neighborhood Sub-Basis
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Definition
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 $\tau$ if and only if:
- for each neighborhood $N$ of $x$, there exists a finite subset $K$ of $\BB$ such that $\bigcap K \subseteq N$.