Near-homeomorphisms on hereditarily indecomposable circle-like continua
type: Item
instance of: scholarly article
title: Near-homeomorphisms on hereditarily indecomposable circle-like continua
zbMATH Open document ID: 0697.54016
author: Kazuhiro Kawamura
published in: Tsukuba Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The reviewer [Proc. Am. Math. Soc. 91, 147-154 (1984; Zbl 0553.54018)] and \textit{M. Smith} [Proc. Am. Math. Soc. 91, 163-166 (1984; Zbl 0511.54020)] have shown that every continuous self-surjection of the pseudo-arc is a near-homeomorphism. The author presents several conditions on inverse limits of simple closed curves for the inverse limit to be hereditarily indecomposable. He then shows that a continuous self-surjection f of an hereditarily indecomposable circularly chainable continuum is a near-homeomorphism if and only if it is a shape equivalence and if and only if it induces an isomorphism on first Čech cohomology. In particular, if f is monotone then it is a near- homeomorphism. An example is constructed of a degree 2 self-surjection of a pseudo-circle which is not a near homeomorphism.
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54F50
Mathematics Subject Classification ID: 54B35
zbMATH DE Number: 4143011
zbMATH Keywords: inverse limits of simple closed curves
zbMATH Keywords: hereditarily indecomposable circularly chainable continuum
zbMATH Keywords: near-homeomorphism
zbMATH Keywords: shape equivalence
zbMATH Keywords: isomorphism on first Čech cohomology
zbMATH Keywords: pseudo-circle
reviewed by: Wayne Lewis
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496161015
OpenAlex ID: W1923604791
DOI: 10.21099/TKBJM/1496161015
description: scientific article; zbMATH DE number 4143011