Une généralisation de la conjecture de point fixe de Schauder

Details Une généralisation de la conjecture de point fixe de Schauder Une généralisation de la conjecture de point fixe de Schauder

2012-01-12

arxiv.org/abs/1201.2586v1

Mathematics

Algebraic Topology

Scientific paper

We prove the following generalisation of Schauder's fixed point conjecture: Let $C_1,...,C_n$ be convex subsets of a Hausdorff topological vector space. Suppose that the $C_i$ are closed in $C=C_1\cup...\cup C_n$. If $f:C\to C$ is a continuous function whose image is contained in a compact subset of $C$, then its Lefschetz number $\Lambda(f)$ is defined. If $\Lambda(f)\ne0$, then $f$ has a fixed point.

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