Cones that are 1/2-homogeneous

A space is 1/2-homogeneous provided that there are exactly two orbits for the action of 2 the group of homeomorphisms of the space onto itself. Let X be a nonempty compact metric space such that the cone over X is 1/2-homogeneous. It is shown that if X is finite-dimensional, then X is an absolute ne...

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Detalles Bibliográficos
Autores: Nadler, SB, Pellicer-Covarrubias, P
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2007
País:México
Institución:Universidad Nacional Autónoma de México
Repositorio:Sistema de Información de la Facultad de Ciencias, UNAM
OAI Identifier:oai:repositorio.fciencias.unam.mx:11154/1167
Acceso en línea:http://hdl.handle.net/11154/1167
Access Level:acceso abierto
Palabra clave:Mathematics
absolute (neighborhood) retract
arc
arc-like
atriodic
circle-like
cone
connected im Kleinen
contimuum
contractible
dendrite
dimension
finite graph
Hilbert cube
homogeneous
1/2-homogeneous
1/n-homogeneous
homotopically labile point
homotop
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spelling Cones that are 1/2-homogeneousNadler, SBPellicer-Covarrubias, PMathematicsabsolute (neighborhood) retractarcarc-likeatriodiccircle-likeconeconnected im Kleinencontimuumcontractibledendritedimensionfinite graphHilbert cubehomogeneous1/2-homogeneous1/n-homogeneoushomotopically labile pointhomotopA space is 1/2-homogeneous provided that there are exactly two orbits for the action of 2 the group of homeomorphisms of the space onto itself. Let X be a nonempty compact metric space such that the cone over X is 1/2-homogeneous. It is shown that if X is finite-dimensional, then X is an absolute neighborhood retract. A general theorem is proved which shows that finite dimensionality is necessary. It is shown that if X is a 1-dimensional continuum or if X does not contain certain types of triods in some nonempty open set, then X is an arc or a simple closed curve (assuming Cone(X) is 1/2-homogeneous). A number of corollaries are derived. Some unanswered questions are stated.2011-01-22T10:26:17Z2011-01-22T10:26:17Z2007info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article0362-1588http://hdl.handle.net/11154/1167115833(1):229-247reponame:Sistema de Información de la Facultad de Ciencias, UNAMinstname:Universidad Nacional Autónoma de Méxicoinstacron:UNAMenHouston Journal of Mathematicsinfo:eu-repo/semantics/openAccessoai:repositorio.fciencias.unam.mx:11154/11672025-09-17T19:20:05Z
dc.title.none.fl_str_mv Cones that are 1/2-homogeneous
title Cones that are 1/2-homogeneous
spellingShingle Cones that are 1/2-homogeneous
Nadler, SB
Mathematics
absolute (neighborhood) retract
arc
arc-like
atriodic
circle-like
cone
connected im Kleinen
contimuum
contractible
dendrite
dimension
finite graph
Hilbert cube
homogeneous
1/2-homogeneous
1/n-homogeneous
homotopically labile point
homotop
title_short Cones that are 1/2-homogeneous
title_full Cones that are 1/2-homogeneous
title_fullStr Cones that are 1/2-homogeneous
title_full_unstemmed Cones that are 1/2-homogeneous
title_sort Cones that are 1/2-homogeneous
dc.creator.none.fl_str_mv Nadler, SB
Pellicer-Covarrubias, P
author Nadler, SB
author_facet Nadler, SB
Pellicer-Covarrubias, P
author_role author
author2 Pellicer-Covarrubias, P
author2_role author
dc.subject.none.fl_str_mv Mathematics
absolute (neighborhood) retract
arc
arc-like
atriodic
circle-like
cone
connected im Kleinen
contimuum
contractible
dendrite
dimension
finite graph
Hilbert cube
homogeneous
1/2-homogeneous
1/n-homogeneous
homotopically labile point
homotop
topic Mathematics
absolute (neighborhood) retract
arc
arc-like
atriodic
circle-like
cone
connected im Kleinen
contimuum
contractible
dendrite
dimension
finite graph
Hilbert cube
homogeneous
1/2-homogeneous
1/n-homogeneous
homotopically labile point
homotop
description A space is 1/2-homogeneous provided that there are exactly two orbits for the action of 2 the group of homeomorphisms of the space onto itself. Let X be a nonempty compact metric space such that the cone over X is 1/2-homogeneous. It is shown that if X is finite-dimensional, then X is an absolute neighborhood retract. A general theorem is proved which shows that finite dimensionality is necessary. It is shown that if X is a 1-dimensional continuum or if X does not contain certain types of triods in some nonempty open set, then X is an arc or a simple closed curve (assuming Cone(X) is 1/2-homogeneous). A number of corollaries are derived. Some unanswered questions are stated.
publishDate 2007
dc.date.none.fl_str_mv 2007
2011-01-22T10:26:17Z
2011-01-22T10:26:17Z
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv 0362-1588
http://hdl.handle.net/11154/1167
1158
identifier_str_mv 0362-1588
1158
url http://hdl.handle.net/11154/1167
dc.language.none.fl_str_mv en
language_invalid_str_mv en
dc.relation.none.fl_str_mv Houston Journal of Mathematics
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv 33(1):229-247
reponame:Sistema de Información de la Facultad de Ciencias, UNAM
instname:Universidad Nacional Autónoma de México
instacron:UNAM
instname_str Universidad Nacional Autónoma de México
instacron_str UNAM
institution UNAM
reponame_str Sistema de Información de la Facultad de Ciencias, UNAM
collection Sistema de Información de la Facultad de Ciencias, UNAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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