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The Metrizability of Spaces whose Diagonals have a Countable Base

Published online by Cambridge University Press:  20 November 2018

John Ginsburg
John Ginsburg*
Affiliation:
University of Manitoba, Department of Mathematics, Winnipeg, Manitoba. R3T 2N2
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Abstract

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It is shown that the diagonal of X has a countable neighborhood base in X × X if and only if X is a metrizable space whose set of non-isolated points is compact.

Keywords

54E35diagonalneighborhood basemetrizabilitycompact
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 4 , 01 December 1977 , pp. 513 - 514
Copyright
Copyright © Canadian Mathematical Society 1977

References

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3. Chaber, J., Conditions which imply compactness in countably compact spaces, to appear.Google Scholar
4. Simon, P., A note on cardinal invariants of square, Comment Math. Univ. Carolinae 14 (1973),205-213.Google Scholar