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<p>We consider the strong porosity of the family of quasicontinuous and cliquish functions in the space of Baire class functions. We show that the family of Baire functions in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathcal{B}}_{\alpha }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">B</mi> <mi>α</mi> </msub> </math></EquationSource> </InlineEquation>-class is strong porous in the family of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\mathcal{B}}_{\beta }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">B</mi> <mi>β</mi> </msub> </math></EquationSource> </InlineEquation>-class for <i>α &lt; β &lt; ω</i><sub>1</sub>.</p>

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On the porosity of Baire class functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月26日

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  • Jacek Hejduk,
  • Gertruda Ivanova

摘要

We consider the strong porosity of the family of quasicontinuous and cliquish functions in the space of Baire class functions. We show that the family of Baire functions in \({\mathcal{B}}_{\alpha }\) B α -class is strong porous in the family of \({\mathcal{B}}_{\beta }\) B β -class for α < β < ω1.