New types of completeness in metric spaces

This paper is devoted to introduce and study two new properties of completeness in the setting of metric spaces. We will call them Bourbaki-completeness and cofinal Bourbaki-completeness. These notions came from new classes of generalized Cauchy sequences appearing when we try to characterize the so...

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Detalles Bibliográficos
Autores: Garrido Carballo, María Isabel, Meroño Moreno, Ana Soledad
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/33655
Acceso en línea:https://hdl.handle.net/20.500.14352/33655
Access Level:acceso abierto
Palabra clave:515.1
Metric spaces
Bourbaki-completeness
cofinal Bourbaki-completeness
Bourbaki-bounded sets
totally-bounded sets
Stone-Cech compactification
uniform paracompactness
Topología
1210 Topología
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oai_identifier_str oai:docta.ucm.es:20.500.14352/33655
network_acronym_str ES
network_name_str España
repository_id_str
spelling New types of completeness in metric spacesGarrido Carballo, María IsabelMeroño Moreno, Ana Soledad515.1Metric spacesBourbaki-completenesscofinal Bourbaki-completenessBourbaki-bounded setstotally-bounded setsStone-Cech compactificationuniform paracompactnessTopología1210 TopologíaThis paper is devoted to introduce and study two new properties of completeness in the setting of metric spaces. We will call them Bourbaki-completeness and cofinal Bourbaki-completeness. These notions came from new classes of generalized Cauchy sequences appearing when we try to characterize the so-called Bourbaki-boundedness in a similar way that Cauchy sequences characterize the totally boundedness. We also study the topological problem of metrizability by means of a Bourbaki-complete or a cofinally Bourbaki-complete metric. At this respect, we obtain results in the line to the classical Cech theorem about the complete metrizability of a metric space X in terms of its Stone-Cech compactification beta X. Finally we give some relationships between these kinds of completeness and some properties related to paracompactness and uniform paracompactness in the framework of metrizable spaces.Suomalainen TiedeakatemiaUniversidad Complutense de Madrid20142014-01-0120142014-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/33655reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 Not available MTM2012-34341open accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/336552026-06-02T12:44:21Z
dc.title.none.fl_str_mv New types of completeness in metric spaces
title New types of completeness in metric spaces
spellingShingle New types of completeness in metric spaces
Garrido Carballo, María Isabel
515.1
Metric spaces
Bourbaki-completeness
cofinal Bourbaki-completeness
Bourbaki-bounded sets
totally-bounded sets
Stone-Cech compactification
uniform paracompactness
Topología
1210 Topología
title_short New types of completeness in metric spaces
title_full New types of completeness in metric spaces
title_fullStr New types of completeness in metric spaces
title_full_unstemmed New types of completeness in metric spaces
title_sort New types of completeness in metric spaces
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 515.1
Metric spaces
Bourbaki-completeness
cofinal Bourbaki-completeness
Bourbaki-bounded sets
totally-bounded sets
Stone-Cech compactification
uniform paracompactness
Topología
1210 Topología
topic 515.1
Metric spaces
Bourbaki-completeness
cofinal Bourbaki-completeness
Bourbaki-bounded sets
totally-bounded sets
Stone-Cech compactification
uniform paracompactness
Topología
1210 Topología
description This paper is devoted to introduce and study two new properties of completeness in the setting of metric spaces. We will call them Bourbaki-completeness and cofinal Bourbaki-completeness. These notions came from new classes of generalized Cauchy sequences appearing when we try to characterize the so-called Bourbaki-boundedness in a similar way that Cauchy sequences characterize the totally boundedness. We also study the topological problem of metrizability by means of a Bourbaki-complete or a cofinally Bourbaki-complete metric. At this respect, we obtain results in the line to the classical Cech theorem about the complete metrizability of a metric space X in terms of its Stone-Cech compactification beta X. Finally we give some relationships between these kinds of completeness and some properties related to paracompactness and uniform paracompactness in the framework of metrizable spaces.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-01-01
2014
2014-01-01
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/20.500.14352/33655
url https://hdl.handle.net/20.500.14352/33655
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 Not available MTM2012-34341
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 Suomalainen Tiedeakatemia
publisher.none.fl_str_mv Suomalainen Tiedeakatemia
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 15,223283

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