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Abstract <p>We investigate resolvability at a point of regular Lindelöf and pseudocompact spaces. We also generalize results of Pytkeev on resolvability and resolvability at a point of regular countably compact spaces. In particular, we prove the following statement. Suppose that a space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11970_2025_7222_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(X\)</EquationSource> <!--BMatMGU2570046Lipin-m1--> </InlineEquation> is regular and every infinite subset of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11970_2025_7222_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(X\)</EquationSource> <!--BMatMGU2570046Lipin-m2--> </InlineEquation> with a cardinality smaller than <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11970_2025_7222_Article_IEq3.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(\kappa&gt;\omega\)</EquationSource> <!--BMatMGU2570046Lipin-m3--> </InlineEquation> has a complete accumulation point. Then <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11970_2025_7222_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(X\)</EquationSource> <!--BMatMGU2570046Lipin-m4--> </InlineEquation> is <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11970_2025_7222_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="107" /> </InlineMediaObject> <EquationSource Format="TEX">\(\min\{\kappa,\Delta(X)\}\)</EquationSource> <!--BMatMGU2570046Lipin-m5--> </InlineEquation>-resolvable.</p>

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Resolvability at a Point and Generalizations of Compactness

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • A. E. Lipin

摘要

Abstract

We investigate resolvability at a point of regular Lindelöf and pseudocompact spaces. We also generalize results of Pytkeev on resolvability and resolvability at a point of regular countably compact spaces. In particular, we prove the following statement. Suppose that a space \(X\) is regular and every infinite subset of \(X\) with a cardinality smaller than \(\kappa>\omega\) has a complete accumulation point. Then \(X\) is \(\min\{\kappa,\Delta(X)\}\) -resolvable.