Description: A space where every open cover has a point-finite subcover is compact. This is significant in part because it shows half of the proposition that if only half the generalization in the definition of metacompactness (and consequently paracompactness) is performed, one does not obtain any more spaces. (Contributed by Jeff Hankins, 21-Jan-2010) (Proof shortened by Mario Carneiro, 11-Sep-2015)
Ref | Expression | ||
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Hypothesis | comppfsc.1 | |
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Assertion | comppfsc | |