Degree of homogeneity on cones
type: Item
instance of: scholarly article
title: Degree of homogeneity on cones
zbMATH Open document ID: 1300.54045
author: Alicia Santiago-Santos
author: Patricia Pellicer-Covarrubias
published in: Topology and its Applications
publication date: 2014-08-27T00:00:00Z
reviewed by: Matej Merhar
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54B15
Mathematics Subject Classification ID: 54F50
zbMATH DE Number: 6334612
zbMATH Keywords: cone
zbMATH Keywords: continuum
zbMATH Keywords: degree of homogeneity
zbMATH Keywords: local dendrite
zbMATH Keywords: orbit
zbMATH Keywords: 1/2-homogeneous
zbMATH Keywords: 1/n-homogeneous
MaRDI profile type: Publication
full work available at URL: j.topol.2014.07.002
OpenAlex ID: W2009842503
cites work: Half-homogeneous chainable continua with end points
cites work: On indecomposable \(\frac {1}{2}\)-homogeneous circle-like continua
cites work: Monotone mappings of universal dendrites
cites work: Dendrites
cites work: Q3162346
cites work: Q4230677
cites work: A family of circle-like, \(\frac{1}{n}\)-homogeneous, indecomposable continua
cites work: Q3304890
cites work: \(\frac 1 2\)-homogeneous suspensions
cites work: 1\over 2-Homogeneous hyperspace suspensions
cites work: Q4064159
cites work: Q4004123
cites work: Hyperspaces with exactly two orbits
cites work: Q5297732
cites work: \(\frac {1}{2}\)-Homogeneous continua with cut points
cites work: On \(\frac 12\)-homogeneous continua
cites work: On 1/2-homogeneous ANR spaces
cites work: \(\frac{1}{2}\)-homogeneity in symmetric products
cites work: \(\frac{1}{2}\)-homogeneity of \(n\)th suspensions
cites work: Half-homogeneous indecomposable circle-like continuum
cites work: Orbits of Higher-Dimensional Hereditarily Indecomposable Continua
cites work: Degree of homogeneity on suspensions
cites work: Q5837858
cites work: Q5605131
DOI: 10.1016/J.TOPOL.2014.07.002
review text: The authors study the degree of homogeneity of the cone of a space \(X\) (the degree of homogeneity of a space \(X\) is the number of orbits for the action of the group of homeomorphisms of \(X\) onto itself).NEWLINENEWLINEThey determine the orbits and the degree of homogeneity of the cone of a space \(X\) in terms of that of \(X\), when \(X\) is either a local dendrite or a Hausdorff space with no arcs. They also analyze how some subsets of \({Cone}(X)\) behave under homeomorphisms of \({Cone}(X)\) onto itself.NEWLINENEWLINEThe paper ends with some open questions regarding the degree of homogeneity for some other classes of continua related to the ones that were studied in it.
description: scientific article; zbMATH DE number 6334612