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<p>Answering a question raised by V.V. Tkachuk in [10], we present several examples of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10474_2025_1521_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-compact spaces, some only consistent and some in ZFC, that are not countably tight but in which the closure of any discrete subset is countably tight. In fact, in some of our examples the closures of all discrete subsets are even first countable.</p>

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Countable tightness is not discretely reflexive in \(\sigma\)-compact spaces

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  • 发表日期：

    2025年3月28日

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  • I. Juhász,
  • J. van Mill

摘要

Answering a question raised by V.V. Tkachuk in [10], we present several examples of \(\sigma\) σ -compact spaces, some only consistent and some in ZFC, that are not countably tight but in which the closure of any discrete subset is countably tight. In fact, in some of our examples the closures of all discrete subsets are even first countable.