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Abstract <p>The question of the existence of a <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8214_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(k\)</EquationSource> <!--LobJMat2560518Allahverdiyeva-m3--> </InlineEquation>-regular embedding of a given finite-dimensional compact metric space <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8214_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(X\)</EquationSource> <!--LobJMat2560518Allahverdiyeva-m4--> </InlineEquation> into a Euclidean space of a given dimension <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8214_Article_IEq5.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(m\)</EquationSource> <!--LobJMat2560518Allahverdiyeva-m5--> </InlineEquation> is studied, i.e., such a continuous mapping that no more than <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8214_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(k\)</EquationSource> <!--LobJMat2560518Allahverdiyeva-m6--> </InlineEquation> points fall on any plane of dimension <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8214_Article_IEq7.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\((k-1)\)</EquationSource> <!--LobJMat2560518Allahverdiyeva-m7--> </InlineEquation>. These mappings are important in the theory of interpolation and approximation.</p>

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Criterion for \(k\)-Regularity of a Mapping in Terms of a Space of Measures

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • S. E. Allahverdiyeva,
  • S. A. Bogatyy

摘要

Abstract

The question of the existence of a \(k\) -regular embedding of a given finite-dimensional compact metric space \(X\) into a Euclidean space of a given dimension \(m\) is studied, i.e., such a continuous mapping that no more than \(k\) points fall on any plane of dimension \((k-1)\) . These mappings are important in the theory of interpolation and approximation.