Category:Neighborhood Bases

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This category contains results about Neighborhood Bases.

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 basis at $x$ if and only if:

For each neighborhood $N$ of $x$, there is an $M \in \BB$ such that $M \subseteq N$.