Fixed-point index for compositions of set-valued maps with proximally \(\infty\)-connected values on arbitrary ANR's
type: Item
instance of: scholarly article
title: Fixed-point index for compositions of set-valued maps with proximally \(\infty\)-connected values on arbitrary ANR's
zbMATH Open document ID: 0846.55001
DOI: 10.1007/BF01026835
author: Ralf Bader
author: Wojciech Kryszewski
published in: Set-Valued Analysis
publication date: 1996-09-25T00:00:00Z
review text: This note presents an integer-valued fixed-point index theory for the class of compositions of maps from the class \(J\) defined on arbitrary ANR's satisfying all axioms. The class \(J\) is contained in the class of compositions of acyclic maps. However, the authors leave open the problem if every acyclic map on an ANR belongs to the class \(J\). Following the introduction which describes earlier attempts to define fixed-point index theory for multivalued maps, the paper is divided into four sections. The first is preparatory, the second recalls Kryszewski's definition of an index on compact ANR's and proves the commutativity, mod \(p\) and multiplicativity of this index, the third is devoted to the construction and study of a fixed-point index of maps on open subsets of normed spaces, and the fourth gives the main results concerning a fixed-point index theory on arbitrary ANR's. They conclude with a discussion on the normalization axiom and the relation of their index with the notion of essential maps (in the sense of Górniewicz, Granas, and the second author).
reviewed by: Zvonko Čerin
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 711403
zbMATH Keywords: ANR
zbMATH Keywords: fixed-point index
Wikidata QID: Q96744855
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 711403