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New results on the aggregation of norms

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New results on the aggregation of norms

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dc.contributor.author Pedraza Aguilera, Tatiana es_ES
dc.contributor.author Rodríguez López, Jesús es_ES
dc.date.accessioned 2022-09-23T18:02:28Z
dc.date.available 2022-09-23T18:02:28Z
dc.date.issued 2021-09 es_ES
dc.identifier.uri http://hdl.handle.net/10251/186518
dc.description.abstract [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. es_ES
dc.description.sponsorship 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. es_ES
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Mathematics es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Norm es_ES
dc.subject Asymmetric norm es_ES
dc.subject Aggregation es_ES
dc.subject Product topology es_ES
dc.subject Supremum topology es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title New results on the aggregation of norms es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/math9182291 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095709-B-C21/ES/METRICAS DIFUSAS Y OPERADORES DE INDISTINGUIBILIDAD: APLICACIONES EN ROBOTICA/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Pedraza Aguilera, T.; Rodríguez López, J. (2021). New results on the aggregation of norms. Mathematics. 9(18):1-19. https://doi.org/10.3390/math9182291 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/math9182291 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 19 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 9 es_ES
dc.description.issue 18 es_ES
dc.identifier.eissn 2227-7390 es_ES
dc.relation.pasarela S\445792 es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.contributor.funder Ministerio de Ciencia, Innovación y Universidades es_ES


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