Presenting the frame of the unit circle

Detalhes bibliográficos
Autor(a) principal: Gutiérrez García, Javier
Data de Publicação: 2016
Outros Autores: Mozo Carollo, Imanol, Picado, Jorge
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/44424
https://doi.org/10.1016/j.jpaa.2015.08.004
Resumo: We present the frame L(T) of the unit circle by generators and relations in two alternative ways. The first is the localic counterpart of the Alexandroff compactification of the real line while the other can be understood as a localic analogue of the quotient space R/Z. With an eye towards a prospective point-free description of Pontryagin duality, we then show how the usual group operations of the frame of reals can be lifted to the new frame L(T), endowing it with a canonical localic group structure.
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spelling Presenting the frame of the unit circleWe present the frame L(T) of the unit circle by generators and relations in two alternative ways. The first is the localic counterpart of the Alexandroff compactification of the real line while the other can be understood as a localic analogue of the quotient space R/Z. With an eye towards a prospective point-free description of Pontryagin duality, we then show how the usual group operations of the frame of reals can be lifted to the new frame L(T), endowing it with a canonical localic group structure.Elsevier2016info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/44424http://hdl.handle.net/10316/44424https://doi.org/10.1016/j.jpaa.2015.08.004https://doi.org/10.1016/j.jpaa.2015.08.004enghttp://www.sciencedirect.com/science/article/pii/S002240491500211XGutiérrez García, JavierMozo Carollo, ImanolPicado, Jorgeinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2021-06-29T10:03:02Zoai:estudogeral.uc.pt:10316/44424Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:23.143547Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Presenting the frame of the unit circle
title Presenting the frame of the unit circle
spellingShingle Presenting the frame of the unit circle
Gutiérrez García, Javier
title_short Presenting the frame of the unit circle
title_full Presenting the frame of the unit circle
title_fullStr Presenting the frame of the unit circle
title_full_unstemmed Presenting the frame of the unit circle
title_sort Presenting the frame of the unit circle
author Gutiérrez García, Javier
author_facet Gutiérrez García, Javier
Mozo Carollo, Imanol
Picado, Jorge
author_role author
author2 Mozo Carollo, Imanol
Picado, Jorge
author2_role author
author
dc.contributor.author.fl_str_mv Gutiérrez García, Javier
Mozo Carollo, Imanol
Picado, Jorge
description We present the frame L(T) of the unit circle by generators and relations in two alternative ways. The first is the localic counterpart of the Alexandroff compactification of the real line while the other can be understood as a localic analogue of the quotient space R/Z. With an eye towards a prospective point-free description of Pontryagin duality, we then show how the usual group operations of the frame of reals can be lifted to the new frame L(T), endowing it with a canonical localic group structure.
publishDate 2016
dc.date.none.fl_str_mv 2016
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10316/44424
http://hdl.handle.net/10316/44424
https://doi.org/10.1016/j.jpaa.2015.08.004
https://doi.org/10.1016/j.jpaa.2015.08.004
url http://hdl.handle.net/10316/44424
https://doi.org/10.1016/j.jpaa.2015.08.004
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv http://www.sciencedirect.com/science/article/pii/S002240491500211X
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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