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We show that, in analysis, many pathological phenomena occur more often than one could expect, that is, in a linear or algebraic way. We show this by means of the construction of large algebraic structures (infinite dimensional vector spaces or [...]texto impreso
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 fun[...]texto impreso
We construct infinite-dimensional Banach spaces and infinitely generated Banach algebras of functions that, except for 0, satisfy some kind of special or pathological property. Three of these structures are: a Banach algebra of everywhere contin[...]texto impreso
We show that some pathological phenomena occur more often than one could expect, existing large algebraic structures (infinite dimensional vector spaces, algebras, positive cones or infinitely generated modules) enjoying certain special properti[...]texto impreso
Aron, R.M. ; García-Pacheco, F.J. ; Pérez García, David ; Seoane-Sepúlveda, Juan B. | Elsevier | 2009A subset M of a topological vector space X is said to be dense-lineable in X if there exists an infinite dimensional linear manifold in M boolean OR {0} and dense in X. We give sufficient conditions for a lineable set to be dense-lineable, and w[...]texto impreso
García-Pacheco, F.J. ; Rambla-Barreno, F. ; Seoane-Sepúlveda, Juan B. | Matematisk Institut, Universitetsparken NY Munkegade | 2008Let 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 bool[...]texto impreso
In this note we study the geometry of drops in Banach spaces, and we use it to characterize two well known geometrical properties: rotundity and smoothness.texto impreso
We give a new and direct proof of the fact that, in any infinite dimensional Banach space, the unit sphere minus any one point is homeomorphic to a closed hyperplane. The proof involves L-structures and geometric concepts as, for instance, rotun[...]texto impreso
We show that there exists an infinite dimensional vector space every non-zero element of which is a non-measurable function. Moreover, this vector space can be chosen to be closed and to have dimension beta for any cardinality beta. Some techniq[...]
