Publication: Lineability and coneability of discontinuous functions on R
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2008
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Kossuth Lajos Tudomanyegyetem
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Abstract
We construct infinite dimensional vector spaces and positive cones of discontinuous functions on R enjoying some special properties, such as functions with an arbitrary F-sigma 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.