Definition:Filter on Set/Filtered Set

Definition

Let $S$ be a set.

Let $\FF$ be a filter on $S$.

Then $S$ is said to be filtered by $\FF$, or just a filtered set.

Sources

• 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