A Tychonoff almost realcompactification

Woods, R. Grant

doi:10.1090/S0002-9939-1974-0331330-4

A Tychonoff almost realcompactification

Author: R. Grant Woods
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
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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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