Order-cushioned refinements and normality

Smith, J. C.; Telgársky, Rastislav

doi:10.1090/S0002-9939-1982-0656127-1

Order-cushioned refinements and normality
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by J. C. Smith and Rastislav Telgársky

Proc. Amer. Math. Soc. 85 (1982), 475-479

DOI: https://doi.org/10.1090/S0002-9939-1982-0656127-1

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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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