Q-linear functions, functions with dense graph, and everywhere surjectivity

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dc.contributor.authorGarcía-Pacheco, F.J.
dc.contributor.authorRambla-Barreno, F.
dc.contributor.authorSeoane Sepúlveda, Juan Benigno
dc.date.accessioned2023-06-20T10:33:07Z
dc.date.available2023-06-20T10:33:07Z
dc.date.issued2008
dc.description.abstractLet L, S and D denote, respectively, the set of Q-linear functions, the set of everywhere surjective functions and the set of dense-graph functions on R. In this note, we show that the sets D \ (S boolean OR L), S \ L, S boolean AND L and D boolean AND L \ S are lineable. Moreover, all these sets contain (omitting zero) a vector space of the biggest possible dimension, 2(c).
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/20044
dc.identifier.issn0025-5521
dc.identifier.officialurlhttp://www.mscand.dk/article.php?id=3080
dc.identifier.urihttps://hdl.handle.net/20.500.14352/50461
dc.issue.number1
dc.journal.titleMathematica Scandinavica
dc.language.isoeng
dc.page.final160
dc.page.initial156
dc.publisherMatematisk Institut, Universitetsparken NY Munkegade
dc.rights.accessRightsrestricted access
dc.subject.cdu517.98
dc.subject.keywordLineability
dc.subject.ucmAnálisis funcional y teoría de operadores
dc.titleQ-linear functions, functions with dense graph, and everywhere surjectivity
dc.typejournal article
dc.volume.number102
dcterms.referencesAron, R.M., García, D., Maestre, M., Linearity in non-linear problems, Rev. R.Acad. Cienc.Exactas Fís. Nat. Ser.A Mat. 95 (2001), 7–12. Aron, R. M., Gurariy, V. I., Seoane-Sepúlveda, J.B.,Lineability and spaceability of sets of functions on R, Proc. Amer. Math. Soc. 133 3 (2005),795–803. Aron, R. M., Seoane-Sepúlveda, J. B., Algebrability of the set of everywhere surjective functions on C, Bull. Belg.Math. Soc. Simon Stevin 14 n. 1 (2007), 25–31. Enflo, P., Gurariy, V. I., On lineability and spaceability of sets in functions spaces, preprint. García-Pacheco, F. J., Palmberg, N., Seoane-Sepúlveda, J.B. Lineability and Algebrability of pathological phenomena in analysis, J. Math. Anal. Appl. 326 n. 2 (2007), 929–939. Gelbaum, B. R., Olmsted, J. M. H., Counterexamples in Analysis, Dover Publications, New York, 2003. Lebesgue, H., Leçons sur l’intégration, Gauthier-Willars,1904.
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