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On Metrizability of Topological Spaces

Published online by Cambridge University Press:  20 November 2018

Carlos J. R. Borges
Carlos J. R. Borges*
Affiliation:
University of California, Davis, California
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Our present work is divided into three sections. In §2 we study the metrizability of spaces with a Gδ-diagonal (see Definition 2.1). In §3 we study the metrization of topological spaces by means of collections of (not necessarily continuous) real-valued functions on a topological space. Our efforts, in §§2 and 3, are directed toward answering the following question: “Is every normal, metacompact (see Definition 2.4) Moore space a metrizable space?” which still remains unsolved. (However, Theorems 2.12 through 2.15 and Theorem 3.1 may be helpful in answering the preceding question.) In §4 we prove an apparently new necessary and sufficient condition for the metrizability of the Stone-Čech compactification of a metrizable space and hence for the compactness of a metric space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 795 - 804
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

This research was supported by NSF Grant GP-4770.

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