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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Resolutions of $H$-closed spaces
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by Louis M. Friedler PDF
Proc. Amer. Math. Soc. 71 (1978), 309-312 Request permission

Abstract:

It is shown that every Hausdorff space X is the perfect, irreducible, continuous image of a Hausdorff space $\tilde X$ which has a basis with open closures. Further, $w(\tilde X) \leqslant w(X)$, where $w(\tilde X)$ represents the weight of X, and if X is H-closed then $\tilde X$ is also H-closed. A corollary of this result is that if $f:X \to Y$ is a continuous map of the H-closed space X onto the semi-regular Hausdorff space Y, then $w(Y) \leqslant w(X)$.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 309-312
  • MSC: Primary 54D25
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0493965-1
  • MathSciNet review: 0493965