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On very non-linear subsets on continuous functions

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dc.contributor.authorBotelho, G.
dc.contributor.authorCariello, D.
dc.contributor.authorFavaro, V.V.
dc.contributor.authorPellegrino, D.
dc.contributor.authorSeoane-Sepúlveda, Juan B.
dc.date.accessioned2023-06-19T13:27:44Z
dc.date.available2023-06-19T13:27:44Z
dc.date.issued2014-09
dc.description.abstractIn this paper, we continue the study initiated by Gurariy and Quarta in 2004 on the existence of linear spaces formed, up to the null vector, by continuous functions that attain the maximum only at one point. Inserting a topological flavor to the subject, we prove that results already known for functions defined on certain subsets of R are actually true for functions on quite general topological spaces. In the line of the original results of Gurariy and Quarta, we prove that, depending on the desired dimension, such subspaces may exist or not.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipCNPq
dc.description.sponsorshipFapemig
dc.description.sponsorshipCNPq-Brazil
dc.description.sponsorshipNCT-Matematica
dc.description.sponsorshipCAPES
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/28237
dc.identifier.doi10.1093/qmath/hat043
dc.identifier.issn0033-5606
dc.identifier.officialurlhttp://qjmath.oxfordjournals.org/content/65/3/841.abstract
dc.identifier.relatedurlhttp://qjmath.oxfordjournals.org
dc.identifier.urihttps://hdl.handle.net/20.500.14352/33770
dc.issue.number3
dc.journal.titleQuarterly journal of mathematics
dc.language.isoeng
dc.page.final850
dc.page.initial841
dc.publisherOxford University Press
dc.relation.projectID302177/2011-6 477124/2012-7
dc.relation.projectIDPPM-00326-13 CEX-APQ-01409/12
dc.relation.projectID245277/2012-9
dc.relation.projectIDMTM2012-34341
dc.rights.accessRightsopen access
dc.subject.cdu517.98
dc.subject.cdu517.51
dc.subject.keywordlineability
dc.subject.keywordcontinuous function
dc.subject.keywordvery non-linear set.
dc.subject.ucmAnálisis funcional y teoría de operadores
dc.titleOn very non-linear subsets on continuous functions
dc.typejournal article
dc.volume.number65
dcterms.references[1] R.M. Aron, V.I. Gurariy, and J.B. Seoane-Sepullveda, lineability and spaceability of sets of functions on R. Proc. Amer. Math. Soc. 133 (2005) 795–803. [2] J. Dugundji, Topology, Allyn and Bacon Inc., Boston, Mass., 1966. [3] V.I. Gurariy and L. Quarta, On the lineability of sets of continuous functions, J. Math. Anal.Appl. 294 (2004), 62–72.
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