On indecomposable \(\frac {1}{2}\)-homogeneous circle-like continua
type: Item
instance of: scholarly article
title: On indecomposable \(\frac {1}{2}\)-homogeneous circle-like continua
zbMATH Open document ID: 1261.54019
author: Jan P. Boronski
published in: Topology and its Applications
publication date: 2013-01-03T00:00:00Z
review text: V.~Neumann-Lara, P.~Pellicer-Covarrubias and I.~Puga-Espinosa in one of their papers described a decomposable \(\frac{1}{2}\)-homogeneous circle-like continuum. In the same paper they asked whether there exists an indecomposable \(\frac{1}{2}\)-homogeneous circle-like continuum. In this paper the author gives the answer to the above question. Furthermore, he proves that there is an uncountable family of topologically distinct indecomposable \(\frac{1}{2}\)-homogeneous circle-like continua. His construction of indecomposable \(\frac{1}{2}\)-homogeneous circle-like continua is based on inverse limits of decomposable \(\frac{1}{2}\)-homogeneous circle-like continua. Each factor space is the \(\frac{1}{2}\)-homogeneous \(n\)-fold covering space of a continuum described by V.~Neumann-Lara, P.~Pellicer-Covarrubias and I.~Puga-Espinosa, the bonding maps are the covering maps and the resulting space is a solenoidal continuum. In the end of the paper he proves that for an indecomposable \(\frac{1}{2}\)-homogeneous circle-like continuum \(Y\) the two orbits of Homeo(\(Y\)) are uncountable.
reviewed by: Matevž Črepnjak
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 6121482
zbMATH Keywords: \(\frac{1}{2}\)-homogeneous
zbMATH Keywords: Circle-like
zbMATH Keywords: Indecomposable continuum
MaRDI profile type: Publication
full work available at URL: j.topol.2012.09.014
OpenAlex ID: W1996033649
DOI: 10.1016/J.TOPOL.2012.09.014
description: scientific article; zbMATH DE number 6121482