Openness of induced mappings
type: Item
instance of: scholarly article
title: Openness of induced mappings
zbMATH Open document ID: 0953.54012
DOI: 10.1016/S0166-8641(99)00042-5
author: Włodzimierz J. Charatonik
author: Alejandro Illanes
author: Janusz J. Charatonik
published in: Topology and its Applications
publication date: 2000-02-08T00:00:00Z
review text: The authors investigate, for a map \(f : X \to Y\) between continua, when the induced map \(C(f): C(X) \to C(Y)\) is open. If \(X\) is either hereditarily locally connected or a fan then \(C(f)\) is open only when \(f\) is a homeomorphism. If \(X\) and \(Y\) are nondegenerate continua and \(f: X \times Y \to X\) is the natural projection, then \(C(f)\) is open only if \(X\) is hereditarily unicoherent. An example is constructed to show that hereditary unicoherence of \(X\) is not a sufficient condition for \(C(f)\) to be open. It is shown that for any dendrite \(X\) and nondegenerate continuum \(Y\) the corresponding map \(C(f)\) is open. Examples are also constructed involving continuous decompositions rather than products. Several examples and open questions are presented.
reviewed by: Wayne Lewis
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54F55
zbMATH DE Number: 1367556
zbMATH Keywords: continuum
zbMATH Keywords: dendrite
zbMATH Keywords: hyperspace
zbMATH Keywords: induced mapping
zbMATH Keywords: open mapping
MaRDI profile type: Publication
full work available at URL: s0166-8641(99)00042-5
OpenAlex ID: W2069124705
description: scientific article; zbMATH DE number 1367556