On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic set

In this work we analyze some topological properties of the remainder partial derivative M := beta(s)*M\M of the semialgebraic Stone-Cech compactification beta(s)*M of a semialgebraic set M subset of R-m in order to 'distinguish' its points from those of M. To that end we prove that the set...

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Detalles Bibliográficos
Autores: Fernando Galván, José Francisco, Gamboa Mutuberria, José Manuel
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:20.500.14352/18252
Acceso en línea:https://hdl.handle.net/20.500.14352/18252
Access Level:acceso abierto
Palabra clave:514
512.7
Rings
Spaces
Geometría
Geometria algebraica
1204 Geometría
1201.01 Geometría Algebraica
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spelling On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic setFernando Galván, José FranciscoGamboa Mutuberria, José Manuel514512.7RingsSpacesGeometríaGeometria algebraica1204 Geometría1201.01 Geometría AlgebraicaIn this work we analyze some topological properties of the remainder partial derivative M := beta(s)*M\M of the semialgebraic Stone-Cech compactification beta(s)*M of a semialgebraic set M subset of R-m in order to 'distinguish' its points from those of M. To that end we prove that the set of points of beta(s)*M that admit a metrizable neighborhood in beta(s)*M equals M-1c boolean OR (Cl beta(s)*M((M) over bar <= 1)\(M) over bar <= 1) where M-1c is the largest locally compact dense subset of M and (M) over bar <= 1 is the closure in M of the set of 1-dimensional points of M. In addition, we analyze the properties of the sets (partial derivative) over capM and (partial derivative) over tildeM of free maximal ideals associated with formal and semialgebraic paths. We prove that both are dense subsets of the remainder partial derivative M and that the differences partial derivative M\(partial derivative) over capM and (partial derivative) over capM\(partial derivative) over tildeM are also dense subsets of partial derivative M. It holds moreover that all the points of (partial derivative) over capM have countable systems of neighborhoods in beta(s)*M.Elsevier Science B.V. (North-Holland)Universidad Complutense de Madrid20182018-01-0120182018-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/18252reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/182522026-06-02T12:44:21Z
dc.title.none.fl_str_mv On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic set
title On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic set
spellingShingle On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic set
Fernando Galván, José Francisco
514
512.7
Rings
Spaces
Geometría
Geometria algebraica
1204 Geometría
1201.01 Geometría Algebraica
title_short On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic set
title_full On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic set
title_fullStr On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic set
title_full_unstemmed On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic set
title_sort On the remainder of the semialgebraic Stone-Cech compactification of a semialgebraic set
dc.creator.none.fl_str_mv Fernando Galván, José Francisco
Gamboa Mutuberria, José Manuel
author Fernando Galván, José Francisco
author_facet Fernando Galván, José Francisco
Gamboa Mutuberria, José Manuel
author_role author
author2 Gamboa Mutuberria, José Manuel
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 514
512.7
Rings
Spaces
Geometría
Geometria algebraica
1204 Geometría
1201.01 Geometría Algebraica
topic 514
512.7
Rings
Spaces
Geometría
Geometria algebraica
1204 Geometría
1201.01 Geometría Algebraica
description In this work we analyze some topological properties of the remainder partial derivative M := beta(s)*M\M of the semialgebraic Stone-Cech compactification beta(s)*M of a semialgebraic set M subset of R-m in order to 'distinguish' its points from those of M. To that end we prove that the set of points of beta(s)*M that admit a metrizable neighborhood in beta(s)*M equals M-1c boolean OR (Cl beta(s)*M((M) over bar <= 1)\(M) over bar <= 1) where M-1c is the largest locally compact dense subset of M and (M) over bar <= 1 is the closure in M of the set of 1-dimensional points of M. In addition, we analyze the properties of the sets (partial derivative) over capM and (partial derivative) over tildeM of free maximal ideals associated with formal and semialgebraic paths. We prove that both are dense subsets of the remainder partial derivative M and that the differences partial derivative M\(partial derivative) over capM and (partial derivative) over capM\(partial derivative) over tildeM are also dense subsets of partial derivative M. It holds moreover that all the points of (partial derivative) over capM have countable systems of neighborhoods in beta(s)*M.
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/20.500.14352/18252
url https://hdl.handle.net/20.500.14352/18252
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 Science B.V. (North-Holland)
publisher.none.fl_str_mv Elsevier Science B.V. (North-Holland)
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 15,300719

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