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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Expandibility and collectionwise normality

Authors: J. C. Smith and L. L. Krajewski
Journal: Trans. Amer. Math. Soc. 160 (1971), 437-451
MSC: Primary 54.20
MathSciNet review: 0284966
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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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Keywords: Expandable, boundedly expandable, almost expandable, discretely expandable, H.C. expandable, hereditarily conservative, paracompact, metacompact, subparacompact, $ \theta $-refinable, metrizable, uniform base, $ M$-space, $ \sigma $-space
Article copyright: © Copyright 1971 American Mathematical Society