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Proceedings of the American Mathematical Society

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

 

 

An embedding characterization of almost realcompact spaces


Authors: Z. Frolík and Chen-tung Liu
Journal: Proc. Amer. Math. Soc. 32 (1972), 294-298
MSC: Primary 54.53
DOI: https://doi.org/10.1090/S0002-9939-1972-0290334-9
MathSciNet review: 0290334
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Abstract: Any Hausdorff space X can be embedded into the product space $ \Pi \{ R_f^ + :f \in {C_ + }(X)\} $, where $ {R^ + }$ is the set of all nonnegative reals with the topology consisting of $ {R^ + }$ and all sets of the form $ \{ x \in {R^ + }:x < a\} ,a \in R$, and $ {C_ + }(X)$ is the set of all continuous functions from X to $ {R^ + }$. Almost realcompact Hausdorff spaces are characterized as maximal Hausdorff subspaces in their closures in the product.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0290334-9
Keywords: Almost realcompact, maximal open filter, maximal Hausdorff subspace, Katětov extension
Article copyright: © Copyright 1972 American Mathematical Society