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

Jean-Marc Bonnisseau, Souhail Chebbi (), Pascal Gourdel () and Hakim Hammami ()
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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 nationale des ponts et chaussées - 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 nationale des ponts et chaussées - 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

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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.

Keywords: fixed points; Borsuk's antipodal Theorem; balanced set; approachable selection; Le théorème de Borsuk antipodal; ensemble balancé; sélection approchable; points fixe (search for similar items in EconPapers)
Date: 2007-12
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00204615v1
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Published in 2007

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Related works:
Working Paper: Borsuk's antipodal and fixed-point theorems for correspondences without convex values (2007)
Working Paper: Borsuk's antipodal and fixed-point theorems for correspondences without convex values (2007)
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