New results on the aggregation of norms

[EN] It is a natural question if a Cartesian product of objects produces an object of the same type. For example, it is well known that a countable Cartesian product of metrizable topological spaces is metrizable. Related to this question, Borsik and Dobos characterized those functions that allow ob...

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Detalhes bibliográficos
Autores: Pedraza Aguilera, Tatiana|||0000-0002-5880-0102, Rodríguez López, Jesús|||0000-0001-5141-9977
Formato: artículo
Fecha de publicación:2021
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/186518
Acesso em linha:https://riunet.upv.es/handle/10251/186518
Access Level:acceso abierto
Palavra-chave:Norm
Asymmetric norm
Aggregation
Product topology
Supremum topology
MATEMATICA APLICADA
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spelling New results on the aggregation of normsPedraza Aguilera, Tatiana|||0000-0002-5880-0102Rodríguez López, Jesús|||0000-0001-5141-9977NormAsymmetric normAggregationProduct topologySupremum topologyMATEMATICA APLICADA[EN] It is a natural question if a Cartesian product of objects produces an object of the same type. For example, it is well known that a countable Cartesian product of metrizable topological spaces is metrizable. Related to this question, Borsik and Dobos characterized those functions that allow obtaining a metric in the Cartesian product of metric spaces by means of the aggregation of the metrics of each factor space. This question was also studied for norms by Herburt and Moszynska. This aggregation procedure can be modified in order to construct a metric or a norm on a certain set by means of a family of metrics or norms, respectively. In this paper, we characterize the functions that allow merging an arbitrary collection of (asymmetric) norms defined over a vector space into a single norm (aggregation on sets). We see that these functions are different from those that allow the construction of a norm in a Cartesian product (aggregation on products). Moreover, we study a related topological problem that was considered in the context of metric spaces by Borsik and Dobos. Concretely, we analyze under which conditions the aggregated norm is compatible with the product topology or the supremum topology in each case.J. Rodríguez-López acknowledges financial support from FEDER/Ministerio de Ciencia, Innovación y Universidades-Agencia Estatal de Investigación Proyecto PGC2018-095709-B-C21. We kindly acknowledge the comments of all the reviewers of this paper which have contributed to improve it.MDPI AGDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería InformáticaEuropean Regional Development FundMinisterio de Ciencia, Innovación y UniversidadesRepositorio Institucional de la Universitat Politècnica de València Riunet20212021-09-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/186518reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-095709-B-C21 METRICAS DIFUSAS Y OPERADORES DE INDISTINGUIBILIDAD: APLICACIONES EN ROBOTICAopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1865182026-06-13T07:49:27Z
dc.title.none.fl_str_mv New results on the aggregation of norms
title New results on the aggregation of norms
spellingShingle New results on the aggregation of norms
Pedraza Aguilera, Tatiana|||0000-0002-5880-0102
Norm
Asymmetric norm
Aggregation
Product topology
Supremum topology
MATEMATICA APLICADA
title_short New results on the aggregation of norms
title_full New results on the aggregation of norms
title_fullStr New results on the aggregation of norms
title_full_unstemmed New results on the aggregation of norms
title_sort New results on the aggregation of norms
dc.creator.none.fl_str_mv Pedraza Aguilera, Tatiana|||0000-0002-5880-0102
Rodríguez López, Jesús|||0000-0001-5141-9977
author Pedraza Aguilera, Tatiana|||0000-0002-5880-0102
author_facet Pedraza Aguilera, Tatiana|||0000-0002-5880-0102
Rodríguez López, Jesús|||0000-0001-5141-9977
author_role author
author2 Rodríguez López, Jesús|||0000-0001-5141-9977
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Informática
European Regional Development Fund
Ministerio de Ciencia, Innovación y Universidades
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Norm
Asymmetric norm
Aggregation
Product topology
Supremum topology
MATEMATICA APLICADA
topic Norm
Asymmetric norm
Aggregation
Product topology
Supremum topology
MATEMATICA APLICADA
description [EN] It is a natural question if a Cartesian product of objects produces an object of the same type. For example, it is well known that a countable Cartesian product of metrizable topological spaces is metrizable. Related to this question, Borsik and Dobos characterized those functions that allow obtaining a metric in the Cartesian product of metric spaces by means of the aggregation of the metrics of each factor space. This question was also studied for norms by Herburt and Moszynska. This aggregation procedure can be modified in order to construct a metric or a norm on a certain set by means of a family of metrics or norms, respectively. In this paper, we characterize the functions that allow merging an arbitrary collection of (asymmetric) norms defined over a vector space into a single norm (aggregation on sets). We see that these functions are different from those that allow the construction of a norm in a Cartesian product (aggregation on products). Moreover, we study a related topological problem that was considered in the context of metric spaces by Borsik and Dobos. Concretely, we analyze under which conditions the aggregated norm is compatible with the product topology or the supremum topology in each case.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-09-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/186518
url https://riunet.upv.es/handle/10251/186518
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-095709-B-C21 METRICAS DIFUSAS Y OPERADORES DE INDISTINGUIBILIDAD: APLICACIONES EN ROBOTICA
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
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
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI AG
publisher.none.fl_str_mv MDPI AG
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,198674

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