Geodesic
Countably Compact Spaces and Martin's Axiom
Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 243-249

Voir la notice de l'article provenant de la source Cambridge University Press

The relationship between compact and countably compact topological spaces has been studied by many topologists. In particular an important question is: “What conditions will make a countably compact space compact?” Conditions which are “covering axioms” have been extensively studied. The best results of this type appear in [19]. We wish to examine countably compact spaces which are separable or perfectly normal. Recall that a space is perfect if and only if every closed subset is a Gδ, and that a space is perfectly normal if and only if it is both perfect and normal. We show that the following statement follows from MA +┐ CH and thus is consistent with the usual axioms of set theory: Every countably compact perfectly normal space is compact. This result is Theorem 3 and can be understood without reading much of what goes before. 
Weiss, William. Countably Compact Spaces and Martin's Axiom. Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 243-249. doi: 10.4153/CJM-1978-023-8
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