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Proceedings of the American Mathematical Society

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

 

 

A space which contains no realcompact dense subspace


Author: Toshiji Terada
Journal: Proc. Amer. Math. Soc. 88 (1983), 162-164
MSC: Primary 54D60; Secondary 54B05, 54B10, 54G20
DOI: https://doi.org/10.1090/S0002-9939-1983-0691300-9
MathSciNet review: 691300
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Abstract: A Tychonoff space which contains no realcompact space as a dense subspace is constructed. Let $ \mathcal{D}\mathcal{R}$ be the class of all spaces which contain some realcompact spaces as dense subspaces. Then, as a consequence of the above result, it follows that $ \mathcal{D}\mathcal{R}$ is not closed-hereditary.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0691300-9
Keywords: Dense subspace, realcompact, $ {G_\delta }$-closed, Oz, $ \sigma $-product
Article copyright: © Copyright 1983 American Mathematical Society