On collectionwise normality of locally compact, normal spaces

Balogh, Zoltán T.

doi:10.1090/S0002-9947-1991-0989571-3

On collectionwise normality of locally compact, normal spaces
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Trans. Amer. Math. Soc. 323 (1991), 389-411 Request permission

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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