The Lefschtz-Hopf theorem for compact maps of ULC spaces
type: Item
instance of: scholarly article
title: The Lefschtz-Hopf theorem for compact maps of ULC spaces
zbMATH Open document ID: 1122.55001
author: Robert Cauty
published in: Journal of Fixed Point Theory and Applications
publication date: 2007-08-10T00:00:00Z
review text: A space \(Y\) is uniformly locally contractible (ULC) if there is a neighborhood \(U\) of the diagonal in the product \(Y \times Y\) and a map \(\lambda : U \times [0,1] \to Y\) such that for every \((x,y) \in U\) and \(t \in [0,1]\), \[ \lambda (x,y,0) = x, \quad \lambda (x,y,1) = y, \quad \lambda (x,x,t) = x. \] The author proves that the Lefschetz-Hopf fixed point theorem holds for compact maps \(f : Y \to Y\) of ULC spaces.
reviewed by: Jan Jaworowski
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 5178574
zbMATH Keywords: Lefschetz-Hopf fixed point theorem
zbMATH Keywords: uniformely locally contractible space
MaRDI profile type: Publication
full work available at URL: s11784-006-0002-5
OpenAlex ID: W2003785207
DOI: 10.1007/S11784-006-0002-5
description: scientific article; zbMATH DE number 5178574