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 :...
| Autores: | , , |
|---|---|
| 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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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 |
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reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname:Universitat Politècnica de València (UPV) |
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Universitat Politècnica de València (UPV) |
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RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
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RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
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