Definition:Filter Basis/Definition 2

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Let $S$ be a set.

Let $\BB$ be a subset of a filter $\FF$ on $S$ such that $\BB \ne \O$.

Then $\BB$ is a filter basis of $\FF$ if and only if:

$\forall U \in \FF: \exists V \in \BB: V \subseteq U$

Generated Filter

$\FF$ is said to be generated by $\BB$.

Also known as

A filter basis is also known as a filter base.

Also see

Linguistic Note

The plural of basis is bases.

This is properly pronounced bay-seez, not bay-siz.