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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

PMEA and first countable, countably paracompact spaces


Author: Dennis K. Burke
Journal: Proc. Amer. Math. Soc. 92 (1984), 455-460
MSC: Primary 54D15; Secondary 54D18, 54E30
DOI: https://doi.org/10.1090/S0002-9939-1984-0759673-7
MathSciNet review: 759673
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Abstract: The Product Measure Extension Axiom is used to prove a "$ \theta $-expandable" type property for first countable, countably paracompact (countably metacompact) spaces. Among other results, it follows (under PMEA) that countably paracompact Moore spaces are metrizable, and first countable, countably paracompact Hausdorff spaces are strongly collectionwise normal with respect to compact sets.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0759673-7
Keywords: Product Measure Extension Axiom, countably paracompact, countably metacompact, Moore space, collectionwise normal
Article copyright: © Copyright 1984 American Mathematical Society