Une généralisation de la conjecture de point fixe de Schauder

2012/01/12 by Robert Cauty, Cauty, Robert
Biochemistry, Genetics and Molecular Biology · Mathematics · #55M20 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Sphingolipid Metabolism and Signaling

paper · pdf · doi:10.48550/arxiv.1201.2586

openalex publication_date 2012/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the following generalisation of Schauder's fixed point conjecture: Let C₁,...,C_n be convex subsets of a Hausdorff topological vector space. Suppose that the C_i are closed in C=C₁∪...∪ C_n. If f:C→ C is a continuous function whose image is contained in a compact subset of C, then its Lefschetz number Λ(f) is defined. If Λ(f)≠0, then f has a fixed point.

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