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This article is cited in 1 scientific paper (total in 1 paper)
Q-compactifications of metric spaces
A. V. Arkhangel'skii
Abstract:
For $Q$-spaces (also called functionally closed or Hunt spaces) there are defined in this paper two new invariants, the $q$-weight and the $q^*$-weight. With the aid of these the following results are obtained.
Theorem 1. {\it If $\tau$ is a nonmeasurable cardinal number and $X$ is a metric space of weight not exceeding $\tau$, then $X$ is homeomorphic to a closed subspace of the product of $\tau^{\aleph_0}$ copies of a real line $R$ $($i.e. X\subset_\mathrm{cl}R^{(\tau^{\aleph_0})})$}.
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Theorem~2. {\it If~$\tau$ is a~nonmeasurable cardinal number and~$X$ is a~complete uniform space whose uniform and topological weights do not exceed~$\tau$, then~$X$ is homeomorphic to a~closed subspace of the product of $\tau^{\aleph_0}$ copies of the real line.}
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Theorem~3. {\it Let~$X$ be paracompact, $bX$~a~Hausdorff compactification of~$X$, and~$\tau$ a~nonmeasurable cardinal number such that the weight of~$X$ does not exceed~$\tau$ and~$X$ is the intersection of a~family of not more than~$\tau$ open subsets of~$bX$. Then~$X$ is homeomorphic to a~closed subspace of the product of $\tau^{\aleph_0}$ copies of the real line.}
Bibliography: 8 titles.
Received: 29.06.1972
Citation:
A. V. Arkhangel'skii, “Q-compactifications of metric spaces”, Mat. Sb. (N.S.), 91(133):1(5) (1973), 78–87; Math. USSR-Sb., 20:1 (1973), 85–94
Linking options:
https://www.mathnet.ru/eng/sm3105https://doi.org/10.1070/SM1973v020n01ABEH001844 https://www.mathnet.ru/eng/sm/v133/i1/p78
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Abstract page: | 268 | Russian version PDF: | 100 | English version PDF: | 2 | References: | 49 |
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