The topological complexity of sets of convex differentiable functions

• Autores: Mohammed Yahdi
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 11, Nº 1, 1998, págs. 79-91
• Idioma: inglés
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• Resumen

  • Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banach space X, equipped with the topology of uniform convergence on bounded subsets of X. We show that the subset of all convex Fréchet-differentiable functions on X, and the subset of all (not necessarily equivalent) Fréchet-differentiable norms on X, reduce every coanalytic set, in particular they are not Borel-sets.