Resumen de Lineability and coneability of discontinuous functions on R

A. Aizpuru, María del Consuelo Pérez Eslava, Francisco Javier García Pacheco , Juan Benigno Seoane Sepúlveda

• 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.