Definition:Finite Intersection Axiom

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Definition

Let $T = \left({S, \tau}\right)$ be a topological space.


Let $T$ be such that:

Every set $V_\alpha$ of closed sets of $T$ such that $\displaystyle \bigcap V_\alpha = \varnothing$ contains a finite subset $V_\beta \subseteq V_\alpha$ such that $\displaystyle \bigcap V_\beta = \varnothing$.


Then $T$ satisfies the finite intersection axiom.


Also see


Sources