Some homotopy classification and extension theorems for the class of compositions of acyclic set-valued maps
type: Item
instance of: scholarly article
title: Some homotopy classification and extension theorems for the class of compositions of acyclic set-valued maps
zbMATH Open document ID: 0849.55010
published in: Bulletin des Sciences Mathématiques
publication date: 1995-11-05T00:00:00Z
review text: The presented paper gives an essential advance in the theory of multivalued mappings, in particular in the homotopy classification both of single valued and multivalued mappings and the fixed point theory. The author generalizes the Hopf homotopy classification theorem and also proved an extension theorem for multivalued mappings. The obtained results give us positive answers to some old questions of the theory of multivalued mappings concerning the validity of the Hopf theorem for acyclic multivalued mappings. The main tools rely on the proved theorem (comp. Theorem 2.17 and also 2.11) stating that a perfect surjection with acyclic fibres induces a bijective transformation of the sets of homotopy classes and constituting an extension of the famous Vietoris-Begle mapping theorem.
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 55M25
Mathematics Subject Classification ID: 55M20
zbMATH DE Number: 812669
zbMATH Keywords: multivalued mappings
zbMATH Keywords: homotopy classification
zbMATH Keywords: fixed point
zbMATH Keywords: Vietoris-Begle mapping theorem
author: Wojciech Kryszewski
reviewed by: Lech Górniewicz
MaRDI profile type: Publication
full work available at URL: a909757k
OpenAlex ID: W2139809753
DOI: 10.1039/A909757K
description: scientific article; zbMATH DE number 812669