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Abstract <p> Various estimates of the Borsuk number are discussed. A method for constructing two-distance counterexamples to Borsuk’s conjecture by using <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((0,1)\)</EquationSource> </InlineEquation>-vectors in spaces with <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(l_p\)</EquationSource> </InlineEquation> metrics is considered. </p>

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On Two-Distance \((0,1)\)-Counterexamples to Borsuk’s Conjecture in \(l_p\) Metrics

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • A. M. Raigorodskii,
  • K. A. Smolenskii

摘要

Abstract

Various estimates of the Borsuk number are discussed. A method for constructing two-distance counterexamples to Borsuk’s conjecture by using \((0,1)\) -vectors in spaces with \(l_p\) metrics is considered.