On Countable Compactness and Sequential Compactness
Copyright policy )On Countable Compactness and Sequential Compactness
If a countably compact T 3 {T_3} space X X can be expressed as a union of less then c c many first countable subspaces, then MA implies that X X is sequentially compact. Also MA implies that every countably compact space of size > c > c is sequentially compact. However, there is a model of ZFC in which ω 1 > c {\omega _1} > c and there is a countably compact, separable T 2 {T_2} space of size ω 1 {\omega _1} , which is not sequentially compact.
Consistency and independence results in general topology, countably compact, separable \(T_ 2\)-space, Martin's Axiom, Compactness, countably compact \(T_ 3\) space, countably compact spaces, sequential compactness, ZFC
Consistency and independence results in general topology, countably compact, separable \(T_ 2\)-space, Martin's Axiom, Compactness, countably compact \(T_ 3\) space, countably compact spaces, sequential compactness, ZFC
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