On the Dedekind completion of function rings

Detalhes bibliográficos
Autor(a) principal: Mozo Carollo, Imanol
Data de Publicação: 2015
Outros Autores: Gutiérrez García, Javier, 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/10316/43901
https://doi.org/10.1515/forum-2012-0095
Resumo: This paper introduces the frame of partially defined real numbers and the lattice-ordered ring of partial real functions on a frame. This is then used to construct the order completion of rings of pointfree continuous real functions. The bounded and integer-valued cases are also analysed. The application of this pointfree approach to the classical case C(X) of the ring of continuous real-valued functions on a topological space X yields a new construction for the Dedekind completion of C(X), considerably more direct and natural than the known procedure using Hausdorff continuous functions.
id RCAP_668168a775c8ea2f35179c7b81da90bf
oai_identifier_str oai:estudogeral.uc.pt:10316/43901
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling On the Dedekind completion of function ringsThis paper introduces the frame of partially defined real numbers and the lattice-ordered ring of partial real functions on a frame. This is then used to construct the order completion of rings of pointfree continuous real functions. The bounded and integer-valued cases are also analysed. The application of this pointfree approach to the classical case C(X) of the ring of continuous real-valued functions on a topological space X yields a new construction for the Dedekind completion of C(X), considerably more direct and natural than the known procedure using Hausdorff continuous functions.De Gruyter2015info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43901http://hdl.handle.net/10316/43901https://doi.org/10.1515/forum-2012-0095https://doi.org/10.1515/forum-2012-0095enghttps://doi.org/10.1515/forum-2012-0095Mozo Carollo, ImanolGutiérrez García, JavierPicado, 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:RCAAP2021-06-29T10:03:34Zoai:estudogeral.uc.pt:10316/43901Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:29.673561Repositório 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 On the Dedekind completion of function rings
title On the Dedekind completion of function rings
spellingShingle On the Dedekind completion of function rings
Mozo Carollo, Imanol
title_short On the Dedekind completion of function rings
title_full On the Dedekind completion of function rings
title_fullStr On the Dedekind completion of function rings
title_full_unstemmed On the Dedekind completion of function rings
title_sort On the Dedekind completion of function rings
author Mozo Carollo, Imanol
author_facet Mozo Carollo, Imanol
Gutiérrez García, Javier
Picado, Jorge
author_role author
author2 Gutiérrez García, Javier
Picado, Jorge
author2_role author
author
dc.contributor.author.fl_str_mv Mozo Carollo, Imanol
Gutiérrez García, Javier
Picado, Jorge
description This paper introduces the frame of partially defined real numbers and the lattice-ordered ring of partial real functions on a frame. This is then used to construct the order completion of rings of pointfree continuous real functions. The bounded and integer-valued cases are also analysed. The application of this pointfree approach to the classical case C(X) of the ring of continuous real-valued functions on a topological space X yields a new construction for the Dedekind completion of C(X), considerably more direct and natural than the known procedure using Hausdorff continuous functions.
publishDate 2015
dc.date.none.fl_str_mv 2015
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/10316/43901
http://hdl.handle.net/10316/43901
https://doi.org/10.1515/forum-2012-0095
https://doi.org/10.1515/forum-2012-0095
url http://hdl.handle.net/10316/43901
https://doi.org/10.1515/forum-2012-0095
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://doi.org/10.1515/forum-2012-0095
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
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
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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
repository.mail.fl_str_mv
_version_ 1799133821606559744

Registros relacionados