Point-countability and compactness

Authors:
H. H. Wicke and J. M. Worrell

Journal:
Proc. Amer. Math. Soc. **55** (1976), 427-431

DOI:
https://doi.org/10.1090/S0002-9939-1976-0400166-X

MathSciNet review:
0400166

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Abstract | References | Additional Information

Abstract: We prove that if a countably compact space has an open cover such that each is in at least one but not more than countably many elements of some , then some finite subcollection of covers . We apply the theorem in proving several metrization theorems for countably compact spaces and discuss consequences of weak -refinability, a concept implicit in the statement of the theorem.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1976-0400166-X

Keywords:
(Countably) compact,
(weakly) -refinable,
(weakly) -refinable,
-space,
quasi-developable space,
-base,
-diagonal,
primitive base,
primitive structures,
diagonal a primitive set of interior condensation

Article copyright:
© Copyright 1976
American Mathematical Society