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JOURNALS // Vestnik Samarskogo Universiteta. Estestvenno-Nauchnaya Seriya // Archive

Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2009 Issue 8(74), Pages 61–66 (Mi vsgu280)

Mathematics

Reznichenko's example is metalindelöf

O. I. Pavlov

Department of Higher and Applied Mathematics, Academy of Labor and Social Relations, Moscow, 117454, Russia

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.

UDC: 515.122

Received: 19.10.2009
Revised: 19.10.2009



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