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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-1982-0656127-1
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 <IMG WIDTH="16" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\theta$">-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