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<p>In this paper, we first prove that for each continuum <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( Z \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>Z</mi> </math></EquationSource> </InlineEquation>, the class of all hereditarily indecomposable continua <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( Y_Z \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Y</mi> <mi>Z</mi> </msub> </math></EquationSource> </InlineEquation> that map onto <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( Z \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>Z</mi> </math></EquationSource> </InlineEquation> by a light map does not admit a common model. Also, for several topological properties previously shown not to be Whitney reversible, we demonstrate that the corresponding classes of continua forming the counterexamples do not admit a common model.</p>

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The Non-existence of Common Models for Certain Classes of Continua

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月4日

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  • Eiichi Matsuhashi

摘要

In this paper, we first prove that for each continuum \( Z \) Z , the class of all hereditarily indecomposable continua \( Y_Z \) Y Z that map onto \( Z \) Z by a light map does not admit a common model. Also, for several topological properties previously shown not to be Whitney reversible, we demonstrate that the corresponding classes of continua forming the counterexamples do not admit a common model.