Limit properties of induced mappings
type: Item
instance of: scholarly article
title: Limit properties of induced mappings
zbMATH Open document ID: 0994.54035
DOI: 10.1016/S0166-8641(98)00096-0
author: Włodzimierz J. Charatonik
author: Janusz J. Charatonik
published in: Topology and its Applications
publication date: 2002-10-08T00:00:00Z
review text: Given a mapping \(f:X\to Y\) between continua \(X\) and \(Y\), let \(2^f: 2^X\to 2^Y\) and \(C(f): C(X)\to C(Y)\) denote the corresponding induced mappings. Let \({\mathcal M}\) be a class of mappings between continua. A general problem which is related to a given mapping and to the two induced mappings is to find all interrelations between the following three statements: (1) \(f\in {\mathcal M}\), (2) \(C(f)\in {\mathcal M}\); and (3) \(2^f\in{\mathcal M}\). There are some papers in which particular results concerning this problem are shown for various classes \({\mathcal M}\) of mappings like open, monotone, confluent and some others. In this paper the authors discuss the problem concerning possible relations between conditions (1)--(3) from one side, and the corresponding conditions in which an admissible class near-\({\mathcal M}\), defined as the class of uniform limits of mappings belonging to \({\mathcal M}\), from the other. Special attention is paid to the classes \({\mathcal M}\) of open and of monotone mappings.
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 1395057
zbMATH Keywords: continuum
zbMATH Keywords: induced mapping
zbMATH Keywords: homeomorphism
zbMATH Keywords: monotone mapping
zbMATH Keywords: open mapping
reviewed by: Shou Lin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1395057