Definition:Finite Intersection Axiom
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $T$ be such that:
- Every set $V_\alpha$ of closed sets of $T$ such that $\ds \bigcap V_\alpha = \O$ contains a finite subset $V_\beta \subseteq V_\alpha$ such that $\ds \bigcap V_\beta = \O$.
Then $T$ satisfies the finite intersection axiom.
Also see
- Do not confuse this with the Finite Intersection Property.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $3$: Compactness: Global Compactness Properties