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Borsuk's antipodal and fixed-point theorems for correspondences without convex values

Author

Listed:
  • Jean-Marc Bonnisseau

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Souhail Chebbi

    (KSU - King Saud University [Riyadh])

  • Pascal Gourdel

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Hakim Hammami

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, Ecole Polytechnique de Tunisie - EPT)

Abstract

We present an extension of Borsuk's antipodal theorem (existence of a zero) for antipodally approachable correspondences without convex values. This result is a generalization of Borsuk-Ulam Theorem and has a fixed-point equivalent formulation.

Suggested Citation

  • Jean-Marc Bonnisseau & Souhail Chebbi & Pascal Gourdel & Hakim Hammami, 2007. "Borsuk's antipodal and fixed-point theorems for correspondences without convex values," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00204615, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00204615
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00204615
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    Keywords

    fixed points; Borsuk's antipodal Theorem; balanced set; approachable selection; Le théorème de Borsuk antipodal; ensemble balancé; sélection approchable; points fixe;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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