The Samuel realcompactification

For a uniform space (X, μ), we introduce a realcompactification of X by means of the family Uμ(X) of all the real-valued uniformly continuous functions on X, in the same way that the known Samuel compactification of the space is given by U∗μ(X) the set of all the bounded functions in Uμ(X). We will...

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Detalles Bibliográficos
Autores: Garrido Carballo, María Isabel, Meroño Moreno, Ana Soledad
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/100629
Acceso en línea:https://hdl.handle.net/20.500.14352/100629
Access Level:acceso abierto
Palabra clave:Uniform space
Realcompactification
Real-valued uniformly continuous function
Samuel realcompactification
Cauchy filter
Bourbaki–Cauchy filter
Bourbaki-completeness
Topología
1210.05 Topología General
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spelling The Samuel realcompactificationGarrido Carballo, María IsabelMeroño Moreno, Ana SoledadUniform spaceRealcompactificationReal-valued uniformly continuous functionSamuel realcompactificationCauchy filterBourbaki–Cauchy filterBourbaki-completenessTopología1210.05 Topología GeneralFor a uniform space (X, μ), we introduce a realcompactification of X by means of the family Uμ(X) of all the real-valued uniformly continuous functions on X, in the same way that the known Samuel compactification of the space is given by U∗μ(X) the set of all the bounded functions in Uμ(X). We will call it “the Samuel realcompactification” by several resemblances to the Samuel compactification. In this paper, we present different ways to construct such realcompactification as well as we study the corresponding problem of knowing when a uniform space is Samuel realcompact, that is, when it (topologically) coincides with its Samuel realcompactification. At this respect, we obtain as main result a theorem of Katětov–Shirota type, given in terms of a property of completeness, recently introduced by the authors, called Bourbaki-completeness.ElsevierUniversidad Complutense de Madrid20182018-01-0120182018-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/100629reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/1006292026-06-02T12:44:21Z
dc.title.none.fl_str_mv The Samuel realcompactification
title The Samuel realcompactification
spellingShingle The Samuel realcompactification
Garrido Carballo, María Isabel
Uniform space
Realcompactification
Real-valued uniformly continuous function
Samuel realcompactification
Cauchy filter
Bourbaki–Cauchy filter
Bourbaki-completeness
Topología
1210.05 Topología General
title_short The Samuel realcompactification
title_full The Samuel realcompactification
title_fullStr The Samuel realcompactification
title_full_unstemmed The Samuel realcompactification
title_sort The Samuel realcompactification
dc.creator.none.fl_str_mv Garrido Carballo, María Isabel
Meroño Moreno, Ana Soledad
author Garrido Carballo, María Isabel
author_facet Garrido Carballo, María Isabel
Meroño Moreno, Ana Soledad
author_role author
author2 Meroño Moreno, Ana Soledad
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv Uniform space
Realcompactification
Real-valued uniformly continuous function
Samuel realcompactification
Cauchy filter
Bourbaki–Cauchy filter
Bourbaki-completeness
Topología
1210.05 Topología General
topic Uniform space
Realcompactification
Real-valued uniformly continuous function
Samuel realcompactification
Cauchy filter
Bourbaki–Cauchy filter
Bourbaki-completeness
Topología
1210.05 Topología General
description For a uniform space (X, μ), we introduce a realcompactification of X by means of the family Uμ(X) of all the real-valued uniformly continuous functions on X, in the same way that the known Samuel compactification of the space is given by U∗μ(X) the set of all the bounded functions in Uμ(X). We will call it “the Samuel realcompactification” by several resemblances to the Samuel compactification. In this paper, we present different ways to construct such realcompactification as well as we study the corresponding problem of knowing when a uniform space is Samuel realcompact, that is, when it (topologically) coincides with its Samuel realcompactification. At this respect, we obtain as main result a theorem of Katětov–Shirota type, given in terms of a property of completeness, recently introduced by the authors, called Bourbaki-completeness.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01
2018
2018-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/100629
url https://hdl.handle.net/20.500.14352/100629
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
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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