Essential extension type maps for general classes of maps
type: Item
instance of: scholarly article
title: Essential extension type maps for general classes of maps
zbMATH Open document ID: 1197.54072
author: Donal O'Regan
published in: Applied Mathematics and Computation
publication date: 2010-07-19T00:00:00Z
review text: Essentiality of admissible (or permissible) multivalued maps in completely regular topological spaces is studied. This complete regularity enables to use the Urysohn function technique. For instance, if \(B=\{x\in \overline{U} : x\in H_t(x) \text{ for some } t\in [0,1]\}\), where \(H\) is an admissible compact homotopy without fixed points on the boundary \(\partial U\) of \(U\), then we can take a function \(\mu:\overline{U}\to [0,1]\) with \(\mu|_B\equiv 1\) and \(\mu|_{\partial U}\equiv 0\), and define \(R(x):=H_{\mu(x)}(x)\). Assuming that \(H_0\) is essential, we obtain a fixed point of \(R\). Obviously, it belongs to \(B\), so \(\mu(x)=1\), and \(x\in H_1(x)\). This proves a continuation result.
reviewed by: Grzegorz Gabor
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 5757607
zbMATH Keywords: essential maps
zbMATH Keywords: fixed points
MaRDI profile type: Publication
full work available at URL: j.amc.2010.04.075
OpenAlex ID: W1975596745
cites work: FIXED POINT THEORY FOR MULTIMAPS IN EXTENSION TYPE SPACES
cites work: Q3836181
cites work: Q4421936
cites work: Q4422397
cites work: Fixed point theory on extension-type spaces and essential maps on topological spaces
cites work: Multivalued \(H\)-essential maps of acyclic type on Hausdorff topological spaces
DOI: 10.1016/J.AMC.2010.04.075
description: scientific article; zbMATH DE number 5757607