A fixed point theorem in o-minimal structures
نویسنده
چکیده
Here we prove an o-minimal fixed point theorem for definable continuous maps on definably compact definable sets, generalizing Brumfiel’s version of the Hopf fixed point theorem for semi-algebraic maps. Résumé Dans cet article nous montrons un théorème de point fixe o-minimal pour les applications définissables continues sur les ensembles définissables et définissablement compacts, qui généralise la version de Brumfiel du théorème de point fixe de Hopf pour les applications semialgébriques. ∗Work done while a post-doctoral research fellow at the Mathematical Institute of the University of Oxford and CMAF Universidade de Lisboa with the support of the FCT grant SFRH/BPD/6015/2001. Current support from the FCT (Fundação para a Ciência e Tecnologia), program POCTI (Portugal/FEDER-EU). MSC: 03C64; 55M20.
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