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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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On the topological completion
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by Howard Curzer and Anthony W. Hager PDF
Proc. Amer. Math. Soc. 56 (1976), 365-370 Request permission

Abstract:

Let $X$ be a Tychonoff space. As is well known, the points of the Stone-Čech compactification $\beta X$ “are” the zero-set ultrafilters of $X$, and the points of the Hewitt real-compactification $\upsilon X$ are the zero-set ultrafilters which are closed under countable intersection. It is shown here that a zero-set ultrafilter is a point of the Dieudonné topological completion $\delta X$ iff the family of complementary cozero sets is $\sigma$-discretely, or locally finitely, additive. From this follows a characterization of those dense embeddings $X \subset Y$ such that each continuous metric space-valued function on $X$ extends over $Y$, and a somewhat novel proof of the Katětov-Shirota Theorem.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 365-370
  • MSC: Primary 54D60
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0415573-9
  • MathSciNet review: 0415573