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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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A Tychonoff almost realcompactification
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by R. Grant Woods PDF
Proc. Amer. Math. Soc. 43 (1974), 200-208 Request permission

Abstract:

Let $X$ be a Tychonoff topological space. A Tychonoff almost realcompact space $aX$ is constructed that contains $X$ as a dense subspace and has the property that if $f:X \to Y$ is continuous and $Y$ is Tychonoff and almost realcompact, then $f$ can be extended continuously to $aX$. Several characterizations of $aX$ are given, and the relationships between $aX$, the Hewitt realcompactification $vX$, and the minimal $c$-realcompactification $uX$ are investigated. Properties of the projective covers of these spaces, and their relation to $vE(X)(E(X)$ denotes the projective cover of $X$), are discussed.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 43 (1974), 200-208
  • MSC: Primary 54D60
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0331330-4
  • MathSciNet review: 0331330