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Vestnik SamGU. Estestvenno-Nauchnaya Ser., 2009, Issue 8(74), Pages 61–66
(Mi vsgu280)
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Mathematics
Reznichenko's example is metalindelöf
O. I. Pavlov Department of Higher and Applied Mathematics, Academy of Labor and Social Relations, Moscow, 117454, Russia
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
We note that a pseudocompact space $X$ that was constructed by E. A. Reznichenko is hereditarily metalindelöf. Moreover, every (hereditarily) metalindelöf space $Y$ can be attached to $X$ (the size of $X$ can vary to accommodate $Y$) so that the resulting space is a (hereditarily) metalindelöf pseudocompact space that contains $Y$ as a closed subset. This example is much simpler than related constructions of a pseudocompact not compact space with a point-countable base that are due to S. Watson and
D. B. Shakhmatov or a metalindelöf pseudocompact not compact space that is due to Ian Tree.
Keywords:
metalindelöf, pseudocompact, closed embedding.
Received: 19.10.2009 Revised: 19.10.2009
Citation:
O. I. Pavlov, “Reznichenko's example is metalindelöf”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2009, no. 8(74), 61–66
Linking options:
https://www.mathnet.ru/eng/vsgu280 https://www.mathnet.ru/eng/vsgu/y2009/i8/p61
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Abstract page: | 211 | Full-text PDF : | 78 | References: | 45 | First page: | 1 |
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