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Corpus ID: 118634747

Une généralisation de la conjecture de point fixe de Schauder

@article{Cauty2012UneGD,
title={Une g{\'e}n{\'e}ralisation de la conjecture de point fixe de Schauder},
author={Robert Cauty},
journal={arXiv: Algebraic Topology},
year={2012}
}

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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