\(\frac 1 2\)-homogeneous suspensions
type: Item
instance of: scholarly article
title: \(\frac 1 2\)-homogeneous suspensions
zbMATH Open document ID: 1183.54016
author: María de Jesús López
author: Alicia Santiago-Santos
author: Patricia Pellicer-Covarrubias
published in: Topology and its Applications
publication date: 2009-12-15T00:00:00Z
review text: A metric continuum \(X\) is said to be \(\frac 1 n\)-homogeneous provided that there are exactly \(n\) orbits for the action of the group of homeomorphisms of the space onto itself. An \(n\)-theta is the suspension of the discrete space with \(n\) points. The authors study metric continua \(X\) for which the suspension \(Sus(X)\) is \(\frac 1 2\)-homogeneous. The main results are: Theorem. Let \(X\) be either a local dendrite or a continuum containing a free arc. Then \(Sus(X)\) is \(\frac 1 2\)-homogeneous if and only if \(X\) is an \(n\)-theta for some positive integer \(n\), different from 2. Theorem. The only dendroid \(X\) for which \(Sus(X)\) is \(\frac 1 2\)-homogeneous is the arc. The authors include the following question. Question. Let \(X\) be a compact metric space such that \(Sus(X)\) is \(\frac 1 2\)-homogeneous. Must \(X\) be either homogeneous or \(\frac 1 2\)-homogeneous? Following the line of the paper, it would be interesting to solve the following problem. Problem. Determine those finite graphs (dendrites, local dendrites, dendroids) \(X\) for which \(Sus(X)\) is \(\frac 1 3\)-homogeneous.
reviewed by: Alejandro Illanes
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54B15
Mathematics Subject Classification ID: 54F35
zbMATH DE Number: 5647967
zbMATH Keywords: continuum
zbMATH Keywords: dendrite
zbMATH Keywords: dendroid
zbMATH Keywords: finite graph
zbMATH Keywords: local dendrite
zbMATH Keywords: suspension
zbMATH Keywords: \(\frac 1 2 \)-homogeneous
zbMATH Keywords: \(\frac 1 n\)-homogeneous
MaRDI profile type: Publication
full work available at URL: j.topol.2009.10.007
OpenAlex ID: W2053549384
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DOI: 10.1016/J.TOPOL.2009.10.007
description: scientific article; zbMATH DE number 5647967