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Abstract <p>We consider generalized sobrifications of approximation spaces and establish that they can be obtained as spaces of basic ideals defined on basic subspaces of the given spaces. As a consequence, we derive generalizations of a series of results on classical sobrifications of approximation spaces. In particular, we show that certain generalized sobrifications of such spaces are homeomorphic to their <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8282_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(d\)</EquationSource> <!--LobJMat2560614Kudryashova-m3--> </InlineEquation>-completions.</p>

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To the Theory of \(\mathsf{H}\)-Sober Spaces: II. Approximation Spaces

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • M. I. Kudryashova,
  • M. V. Schwidefsky

摘要

Abstract

We consider generalized sobrifications of approximation spaces and establish that they can be obtained as spaces of basic ideals defined on basic subspaces of the given spaces. As a consequence, we derive generalizations of a series of results on classical sobrifications of approximation spaces. In particular, we show that certain generalized sobrifications of such spaces are homeomorphic to their \(d\) -completions.