Definition:Filter Basis/Generated Filter
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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 $\BB$.
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Filters