Expansive homeomorphisms and plane separating continua
type: Item
instance of: scholarly article
title: Expansive homeomorphisms and plane separating continua
zbMATH Open document ID: 1145.54037
author: Christopher Mouron
published in: Topology and its Applications
publication date: 2008-05-15T00:00:00Z
review text: A homeomorphism \(h: X\to X\) of a metric space \((X,d)\) onto itself is said to be expansive if there exists a constant \(c> 0\) and for any distinct points \(x,y\in X\) there exists an integer \(n\), such that \(d(h^n(x),h^n(y))> c\). It is shown that if \(X\) is a one-dimensional continuum that separates the plane into two pieces, then \(h\) cannot be expansive. The corresponding statement is still unknown for 3-separating plane continua. Another question which remains to be answered is: Does there exist a 2-dimensional non-separating plane continuum that admits an expansive homeomorphism?
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 54F50
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 5275723
zbMATH Keywords: expansive homeomorphism
zbMATH Keywords: 1-cyclic continuum
zbMATH Keywords: plane separating continuum
reviewed by: Ludvík Janoš
MaRDI profile type: Publication
full work available at URL: j.topol.2008.01.003
OpenAlex ID: W1970156494
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DOI: 10.1016/J.TOPOL.2008.01.003
description: scientific article; zbMATH DE number 5275723