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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On collectionwise normality of locally compact, normal spaces


Author: Zoltán T. Balogh
Journal: Trans. Amer. Math. Soc. 323 (1991), 389-411
MSC: Primary 54D15; Secondary 03E35, 03E55, 54A35, 54D45
MathSciNet review: 989571
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Abstract: We prove that by adjoining supercompact many Cohen or random reals to a model of ZFC set theory, in the resulting model, every normal locally compact space is collectionwise normal. In the same models, countably paracompact, locally compact $ {T_3}$-spaces are expandable. Local compactness in the above theorems can be weakened to being of point-countable type, a condition that is implied by both Čech-completeness and first countability.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-0989571-3
PII: S 0002-9947(1991)0989571-3
Keywords: Random and Cohen reals, forcing, supercompact cardinals, locally compact, collectionwise normal, normal Moore space conjecture, countably paracompact
Article copyright: © Copyright 1991 American Mathematical Society