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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 1982, Number 6, Pages 21–28
(Mi vmumm3583)
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This article is cited in 2 scientific papers (total in 2 papers)
Mathematics
Everywhere dense subspaces of topological products and properties associated with final compactness
A. V. Arkhangel'skii, D. V. Ranchin
Abstract:
We prove the following. The $\sigma$–product of a family $\mathfrak{U}$ of topological spaces with countable base is a Lindelöf $\Sigma$-space if and only if $\mathfrak{U}$ has at most $2^{\aleph_0}$ non-homeomorphic elements. The $\sigma$-product of $\mathscr{K}$-analytical spaces is itself $\mathscr{K}$-analytical. Let $X$ be a $\sigma$-product of Lindelöf $\Sigma$-spaces and $C_p(X)$ the space of all continuous real-valued functions on $X$ in the topology of pointwise convergence. Then every bicompact $f\subset C_p(X)$ is a Frechet–Uryson space.
Received: 30.12.1981
Citation:
A. V. Arkhangel'skii, D. V. Ranchin, “Everywhere dense subspaces of topological products and properties associated with final compactness”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1982, no. 6, 21–28
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https://www.mathnet.ru/eng/vmumm3583 https://www.mathnet.ru/eng/vmumm/y1982/i6/p21
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Abstract page: | 60 | Full-text PDF : | 22 |
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