A space which contains no realcompact dense subspace
HTML articles powered by AMS MathViewer
- by Toshiji Terada
- Proc. Amer. Math. Soc. 88 (1983), 162-164
- DOI: https://doi.org/10.1090/S0002-9939-1983-0691300-9
- PDF | Request permission
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.References
- Robert L. Blair and Anthony W. Hager, Extensions of zero-sets and of real-valued functions, Math. Z. 136 (1974), 41โ52. MR 385793, DOI 10.1007/BF01189255
- Robert L. Blair, Spaces in which special sets are $z$-embedded, Canadian J. Math. 28 (1976), no.ย 4, 673โ690. MR 420542, DOI 10.4153/CJM-1976-068-9
- E. V. ล ฤepin, Topological products, groups, and a new class of spaces that are more general than metric spaces, Dokl. Akad. Nauk SSSR 226 (1976), no.ย 3, 527โ529 (Russian). MR 0405350
- Toshiji Terada, Note on $z-$, $C^{\ast } -$, and $C$-embedding, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 13 (1975), no.ย 347-365, 129โ132. MR 391005 โ, Dense subspaces of topological spaces (submitted).
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- 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