Search 205,544,639 papers from all fields of science

Search

Sign InCreate Free Account

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.

In this paper we are interested in a new type of {\it mean-field}, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the… Expand

We ask the question “when will natural selection on a gene in a spatially structured population cause a detectable trace in the patterns of genetic variation observed in the contemporary population?”… Expand

This paper introduces economists to some fixed point theorems for discontinuous mappings with non-convex images on a non-convex domain. These theorems have recently been developed based on a new… Expand

We introduce the class of algebraic ANRs. It is defined by replacing continuous maps by chain mappings in Lefschetz’s characterization of ANRs. To a large extent, the theory of algebraic ANRs… Expand

Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected… Expand

The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.