Atomicity of mappings
type: Item
instance of: scholarly article
title: Atomicity of mappings
zbMATH Open document ID: 0956.54017
DOI: 10.1155/S016117129800101X
author: Włodzimierz J. Charatonik
author: Janusz J. Charatonik
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1998-12-06T00:00:00Z
full work available at URL: https://eudml.org/doc/48659
review text: Summary: A mapping \(f:X\to Y\) between continua \(X\) and \(Y\) is said to be atomic at a subcontinuum \(K\) of the domain \(X\) provided that \(f(K)\) is nondegenerate and \(K=f^{-1}(f(K))\). The set of subcontinua at which a given mapping is atomic, considered as a subspace of the hyperspace of all subcontinua of \(X\), is studied. The introduced concept is applied to get new characterizations of atomic and monotone mappings. Some related questions are asked.
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54B15
zbMATH DE Number: 1230049
zbMATH Keywords: composition factor property
zbMATH Keywords: contratomic
zbMATH Keywords: atomic at a subcontinuum
zbMATH Keywords: hyperspace of all subcontinua
zbMATH Keywords: monotone mappings
MaRDI profile type: Publication
OpenAlex ID: W1983002249
description: scientific article; zbMATH DE number 1230049