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.
@article{urn:eudml:doc:44479,
title = {The topological complexity of sets of convex differentiable functions.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {11},
year = {1998},
pages = {79-91},
zbl = {0906.46014},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44479}
}
Yahdi, Mohammed. The topological complexity of sets of convex differentiable functions.. Revista Matemática de la Universidad Complutense de Madrid, Tome 11 (1998) pp. 79-91. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44479/