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From countable compactness to absolute countable compactness. (English) Zbl 0984.54027

Summary: We show that every countably compact space which is monotonically normal, almost 2-fully normal, radial \(T_2\), or \(T_3\) with countable spread is absolutely countably compact. For the first two mentioned properties, we prove more general results not requiring countable compactness. We also prove that every monotonically normal, orthocompact space is finitely fully normal.

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54A35 Consistency and independence results in general topology
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