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
- DOI: 10.5209/rev_rema.1998.v11.n1.17300
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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.
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