Definition:Finite Intersection Property
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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.
- Do not confuse this with the Finite Intersection Axiom.
- 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