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Proceedings of the American Mathematical Society

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



Order-cushioned refinements and normality

Authors: J. C. Smith and Rastislav Telgársky
Journal: Proc. Amer. Math. Soc. 85 (1982), 475-479
MSC: Primary 54D15; Secondary 54D20
MathSciNet review: 656127
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Abstract: The authors use the notions of order-cushioned covers and weak $ \theta $-covers to obtain the following result.

Theorem. A space $ X$ is collectionwise normal iff every weak $ \theta $-cover of $ X$ has an order-cushioned open refinement.

Similar characterizations are obtained for normal, countably paracompact spaces and analogous embedding theorems are shown.

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Keywords: Paracompact, collectionwise normal, normal, countably paracompact, weak $ \theta $-cover, order locally finite, order closure-preserving, order-cushioned, locally finite, point finite, star-countable, shrinkable, cushioned, embedded
Article copyright: © Copyright 1982 American Mathematical Society