Some properties of minimal S(α) and S(α)FC spaces

2011/12/22 by Alexander V. Osipov, Osipov, Alexander V.
Mathematics · #54B10 #54D25 #54D45 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:54B10 #msc:54D25 #msc:54D45

paper · pdf · doi:10.48550/arxiv.1112.5261

16 pages, 1 figure

arxiv created 2011/12/22 · arxiv updated 2011/12/23

Abstract

A S(n)-space is S(n)-functionally compact (S(n)FC) if every continuous function onto a S(n)-space is closed. S(n)-closed, S(n)-θ-closed, minimal S(n) and S(n)FC spaces are characterized in terms of θ(n)-complete accumulation points. In paper we also give new characteristics of R-closed and regular functionally compact spaces. Results obtained to answer some questions raised by D.Dikranjan, E.Giuli, L.Friedler, M.Girou, D.Pettey and J.Porter.

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