Lineability and coneability of discontinuous functions on R

• Autores: A. Aizpuru, María del Consuelo Pérez Eslava, Francisco Javier García Pacheco, Juan Benigno Seoane Sepúlveda
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 72, Fasc. 1-2, 2008, págs. 129-140
• Idioma: inglés
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• Resumen

  • We construct in¯nite dimensional vector spaces and positive cones of discontinuous functions on R enjoying some special properties, such as functions with an arbitrary F¾ set of points of discontinuity, discontinuous Riemann-integrable functions, or functions having either jump or removable discontinuities at a given point. We show that these special phenomena occur more often than one could expect, i.e. in a linear or algebraic way.