Expansive homeomorphisms and indecomposable subcontinua
type: Item
instance of: scholarly article
title: Expansive homeomorphisms and indecomposable subcontinua
zbMATH Open document ID: 1018.54029
DOI: 10.1016/S0166-8641(02)00002-0
author: Christopher Mouron
published in: Topology and its Applications
publication date: 2003-04-02T00:00:00Z
review text: A compact, connected metric space is called a continuum. It is called \(k\)-cyclic if there exist finite open covers of arbitrary small diameter such that their nerve has at most \(k\) simple closed curves (the nerve of a cover is a graph having its elements as vertices and edges from \(U\) to \(V\) if \(U\cap V \neq\emptyset)\). \textit{H. Kato} [Fundam. Math. 139, 49-57 (1991; Zbl 0823.54028)] posed the question whether a continuum which admits an expansive homeomorphism contains a nondegenerate indecomposable subcontinuum. The paper under review gives a positive answer to this question in case of a \(k\)-cyclic continuum.
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37B45
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54F50
zbMATH DE Number: 1891196
zbMATH Keywords: Expansive homeomorphism
zbMATH Keywords: Indecomposable continuum
zbMATH Keywords: Finitely cyclic
zbMATH Keywords: Tranche
reviewed by: Manfred Denker
MaRDI profile type: Publication
cites work: Expansive homeomorphisms in continuum theory
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cites work: Q3304890
cites work: On the geometry of hyperbolic attractors of smooth cascades
cites work: A Note on Unstable Homeomorphisms
description: scientific article; zbMATH DE number 1891196