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We prove that, in any o-minimal structure, definable C-r mappings can always be approximated by definable Cr+1 mappings. As an application we obtain definable triviality for pairs of definable proper submersions.texto impreso
It was proved recently that a Banach space fails the Mazur intersection property if and only if the family of all closed, convex and bounded subsets which are intersections of balls is uniformly very porous. This paper deals with the geometrical[...]texto impreso
The connected groups acting by isometries on either the real or the complex hyperbolic spaces are determined. A Lie-theoretic description of the homogeneous Riemannian, respectively Kähler, structures of linear type on these spaces is then found[...]texto impreso
As the authors of this article state, "the ordinary functional analyst is naturally impatient with the multiplicity of definitions of `integral' which have been proposed for vector-valued functions, and would much prefer to have a single canonic[...]texto impreso
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The author studies the hereditary Dunford-Pettis property for spaces CX(K) of continuous Xvalued functions (X a Banach space) on a compact Hausdorff space K. First, she shows that CX(K) has the hereditary Dunford-Pettis property if and only if o[...]texto impreso
Acquistapace, Francesca ; Andradas Heranz, Carlos ; Broglia, Fabrizio | University of Illinois | 2002In this note we prove two Positivstellensatze for definable functions of class C-r, 0 less than or equal to r