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$ C$-embedded subsets of products


Author: N. Noble
Journal: Proc. Amer. Math. Soc. 31 (1972), 613-614
DOI: https://doi.org/10.1090/S0002-9939-1972-0284978-8
MathSciNet review: 0284978
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Abstract | References | Additional Information

Abstract: It is shown that each dense subset of $ {R^\mathfrak{n}}$ is $ z$-embedded, from which it follows that a dense subset is $ C$-embedded if and only if it is $ {G_\delta }$-dense. These results extend to, for example, all products of separable metric spaces.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0284978-8
Keywords: $ z$-embedded subsets, $ C$-embedded subsets, product spaces, Hewitt realcompactification
Article copyright: © Copyright 1972 American Mathematical Society

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