# Definition:Filter Basis/Generated Filter

(Redirected from Definition:Generated Filter)

## Definition

Let $S$ be a set.

Let $\powerset S$ be the power set of $S$.

Let $\BB \subset \powerset S$ be a filter basis of a filter $\FF$ on $S$.

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

## Also known as

A filter generated by $\BB$ is also known as a filter spanned by $\BB$.