From countable compactness to absolute countable compactness

Rudin, Mary; Stares, Ian; Vaughan, Jerry

doi:10.1090/S0002-9939-97-04030-6

From countable compactness to absolute countable compactness
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by Mary Ellen Rudin, Ian S. Stares and Jerry E. Vaughan PDF

Proc. Amer. Math. Soc. 125 (1997), 927-934 Request permission

Abstract:

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.

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