Induced MO-mappings
type: Item
instance of: scholarly article
title: Induced MO-mappings
zbMATH Open document ID: 0957.54006
author: Włodzimierz J. Charatonik
author: Janusz J. Charatonik
published in: Tsukuba Journal of Mathematics
publication date: 2000-03-27T00:00:00Z
review text: All spaces are metrizable. The authors study the general question how properties of induced hyperspace maps can be translated in terms of properties of the original map, and vica versa. A continuous function \(f: X\to Y\) is said to be an MO-mapping provided that it can be written in the form \(f= f_1\circ f_2\) such that \(f_1\) is open and \(f_2\) is monotone. Similarly for OM. It is known that if \(f: X\to Y\) is surjective and continuous, then \(f\) is OM iff \(2^f\) is OM iff \(C(f)\) is OM. For MO the situation is different. The authors prove that if \(f\) is MO then so is \(2^f\). The converse is an open problem. For \(C(f)\) a similar result does not hold. They present examples of open maps \(f\) from \([0,1]\) onto itself such that \(C(f)\) is not MO.
reviewed by: Jan van Mill
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 1394751
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496163871
OpenAlex ID: W1898289060
DOI: 10.21099/TKBJM/1496163871
description: scientific article; zbMATH DE number 1394751