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

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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

Suggested Citation

  • Jean-Marc Bonnisseau & Souhail Chebbi & Pascal Gourdel & Hakim Hammami, 2007. "Borsuk's antipodal and fixed-point theorems for correspondences without convex values," Documents de travail du Centre d'Economie de la Sorbonne b07077, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:b07077
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    Keywords

    Borsuk's antipodal Theorem; balanced set; approachable selection; fixed points;
    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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