Partial actions of groups on profinite spaces

[EN] We show that for a partial action η with closed domain of a compact group G on a profinite space X the space of orbits X/~G is profinite, this leads to the fact that when G is profinite the enveloping space XG is also profinite. Moreover, we provide conditions for the induced quotient map πG :...

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Autores: Martínez, Luis, Tapia, Héctor Pinedo, Villamizar, Andrés
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/203789
Acceso en línea:https://riunet.upv.es/handle/10251/203789
Access Level:acceso abierto
Palabra clave:Partial action
Profinite space
Orbit equivalence relation
Clopen sets
Globalization
Continuous section
Reflective subcategory
Enveloping action
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spelling Partial actions of groups on profinite spacesMartínez, LuisTapia, Héctor PinedoVillamizar, AndrésPartial actionProfinite spaceOrbit equivalence relationClopen setsGlobalizationContinuous sectionReflective subcategoryEnveloping action[EN] We show that for a partial action η with closed domain of a compact group G on a profinite space X the space of orbits X/~G is profinite, this leads to the fact that when G is profinite the enveloping space XG is also profinite. Moreover, we provide conditions for the induced quotient map πG : X → X / ∼G of η to have a continuous section. Relations between continuous sections of πG and continuous sections of the quotient map induced by the enveloping action of η are also considered. At the end of this work, we prove that the category of actions on profinite spaces with countable number of clopen sets is reflective in the category of actions of compact Hausdorff spaces having countable number of clopen sets.The first author was supported by CONAHCYT (México).Universitat Politècnica de ValènciaConsejo Nacional de Humanidades, Ciencias y Tecnologías, MéxicoRepositorio Institucional de la Universitat Politècnica de València Riunet20242024-04-02journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/203789reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Compartir igual (by-nc-sa) http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2037892026-06-13T07:49:27Z
dc.title.none.fl_str_mv Partial actions of groups on profinite spaces
title Partial actions of groups on profinite spaces
spellingShingle Partial actions of groups on profinite spaces
Martínez, Luis
Partial action
Profinite space
Orbit equivalence relation
Clopen sets
Globalization
Continuous section
Reflective subcategory
Enveloping action
title_short Partial actions of groups on profinite spaces
title_full Partial actions of groups on profinite spaces
title_fullStr Partial actions of groups on profinite spaces
title_full_unstemmed Partial actions of groups on profinite spaces
title_sort Partial actions of groups on profinite spaces
dc.creator.none.fl_str_mv Martínez, Luis
Tapia, Héctor Pinedo
Villamizar, Andrés
author Martínez, Luis
author_facet Martínez, Luis
Tapia, Héctor Pinedo
Villamizar, Andrés
author_role author
author2 Tapia, Héctor Pinedo
Villamizar, Andrés
author2_role author
author
dc.contributor.none.fl_str_mv Consejo Nacional de Humanidades, Ciencias y Tecnologías, México
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Partial action
Profinite space
Orbit equivalence relation
Clopen sets
Globalization
Continuous section
Reflective subcategory
Enveloping action
topic Partial action
Profinite space
Orbit equivalence relation
Clopen sets
Globalization
Continuous section
Reflective subcategory
Enveloping action
description [EN] We show that for a partial action η with closed domain of a compact group G on a profinite space X the space of orbits X/~G is profinite, this leads to the fact that when G is profinite the enveloping space XG is also profinite. Moreover, we provide conditions for the induced quotient map πG : X → X / ∼G of η to have a continuous section. Relations between continuous sections of πG and continuous sections of the quotient map induced by the enveloping action of η are also considered. At the end of this work, we prove that the category of actions on profinite spaces with countable number of clopen sets is reflective in the category of actions of compact Hausdorff spaces having countable number of clopen sets.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-04-02
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/203789
url https://riunet.upv.es/handle/10251/203789
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Compartir igual (by-nc-sa)
http://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Compartir igual (by-nc-sa)
http://creativecommons.org/licenses/by-nc-sa/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de València
publisher.none.fl_str_mv Universitat Politècnica de València
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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