Definition:Finite Intersection Property

Definition

Let $\Bbb S$ be a set of sets.

Let $\Bbb S$ have the property that:

the intersection of any finite number of sets in $\Bbb S$ is not empty.

Then $\Bbb S$ satisfies the finite intersection property.

Also see

• Do not confuse this with the Finite Intersection Axiom.

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