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

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Author Info
Jean-Marc Bonnisseau () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)
Souhail Chebbi () (King Saud University - Faculty of Sciences de Bizerte)
Pascal Gourdel () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)
Hakim Hammami () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, 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.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00204615_v1.

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Date of creation: Dec 2007
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Handle: RePEc:hal:cesptp:halshs-00204615_v1

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Related research
Keywords: Borsuk's antipodal Theorem; balanced set; approachable selection; fixed points.;

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