# RÉTRACTES ABSOLUS DE VOISINAGE ALGÉBRIQUES

@inproceedings{Cauty2010RETRACTESAD, title={RÉTRACTES ABSOLUS DE VOISINAGE ALGÉBRIQUES}, author={Robert Cauty}, year={2010} }

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 parallels the classical theory of ANRs. Every ANR is an algebraic ANR, but the class of algebraic ANRs is much larger; the most striking difference between these classes is that every locally equiconnected metrisable space is an algebraic ANR, whereas there exist metric linear spaces which are not ARs…

## 5 Citations

### Points fixes des applications compactes dans les espaces ULC

- Mathematics
- 2010

A topological space is locally equiconnected if there exists a neighborhood $U$ of the diagonal in $X\times X$ and a continuous map $\lambda:U\times[0,1]\to X$ such that $\lambda(x,y,0)=x$,…

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

- Mathematics
- 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…

### A proof of the asymptotic conjecture

- Mathematics
- 2021

In this paper we prove that if f is a self-mapping of a nonempty subset K of a normed space X that satisfies some mild conditions, then the minimal displacement of large iterations f n always…

### ON THE BEGINNING OF TOPOLOGY IN LWÓW POCZĄTKI TOPOLOGII WE LWOWIE

- Mathematics
- 2016

We provide one of the first surveys of results in the area of topology by representatives of the Lvov School of mathematics and mathematicians related to the University of Lvov. Viewed together,…

### Key moments of the mutual influence of the Polish and Soviet schools of nonlinear functional analysis in the 1920s--1950s

- Mathematics
- 2018

The paper includes key aspects of the history of development of qualitative methods of non-linear functional analysis (fixed point theorems, theory of mapping degree, theory of Orlicz spaces), within…

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