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Proceedings of the American Mathematical Society

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

 

 

A Tychonoff almost realcompactification


Author: R. Grant Woods
Journal: Proc. Amer. Math. Soc. 43 (1974), 200-208
MSC: Primary 54D60
MathSciNet review: 0331330
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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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DOI: https://doi.org/10.1090/S0002-9939-1974-0331330-4
Keywords: Almost realcompactification, Tychonoff space, projective cover, $ c$-realcompactification
Article copyright: © Copyright 1974 American Mathematical Society