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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Perfect maps of symmetrizable spaces
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by Harold W. Martin
Proc. Amer. Math. Soc. 38 (1973), 410-412
DOI: https://doi.org/10.1090/S0002-9939-1973-0314009-3

Abstract:

It is shown that if $f:X \to Y$ is a perfect map from a symmetrizable space $X$ onto a space $Y$, then $Y$ is metrizable if and only if $f$ is a coherent map. This fact, together with certain known results, yields the following: Let $f:X \to Y$ be a perfect map from a Hausdorff symmetrizable space $X$ onto a space $Y$; the following are equivalent: (1) $X$ is metrizable; (2) $f$ is a regular map; (3) $f$ is a coherent map; (4) $Y$ is metrizable.
References
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Bibliographic Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 38 (1973), 410-412
  • MSC: Primary 54E35
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0314009-3
  • MathSciNet review: 0314009