Expandibility and collectionwise normality

Smith, J. C.; Krajewski, L. L.

doi:10.1090/S0002-9947-1971-0284966-5

Expandibility and collectionwise normality
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by J. C. Smith and L. L. Krajewski PDF

Trans. Amer. Math. Soc. 160 (1971), 437-451 Request permission

Abstract:

In 1958 M. Katětov proved that in a normal space $X,X$ is expandable if and only if $X$ is collectionwise normal and countably paracompact. This result has since been used to answer many questions in various areas of general topology. In this paper Katětov’s theorem is generalized for nonnormal spaces and various characterizations of collectionwise normality are shown. Results concerning metrization, paracompactness, sum theorems, product theorems, mapping theorems and $M$-spaces are then obtained as applications of these new theorems.

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