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arXiv · 1201.2586

Une généralisation de la conjecture de point fixe de Schauder

Robert Cauty
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Abstract

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 $Λ(f)$ is defined. If $Λ(f)\ne0$, then $f$ has a fixed point.

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Robert Cauty. 2012-01-12. Une généralisation de la conjecture de point fixe de Schauder. https://arxiv.org/abs/1201.2586

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