The topological complexity of sets of convex differentiable functions.

Yahdi, Mohammed. "The topological complexity of sets of convex differentiable functions.." Revista Matemática Complutense 11.1 (1998): 79-91. <http://eudml.org/doc/44479>.

@article{Yahdi1998,
abstract = {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.},
author = {Yahdi, Mohammed},
journal = {Revista Matemática Complutense},
keywords = {Funciones continuas; Funciones convexas; Espacios de Banach; Espacios de Frechet; Funciones diferenciables; topology of uniform convergence on bounded subsets; Polish space; analytic subset; Gâteaux differentiable; Fréchet-differentiable},
language = {eng},
number = {1},
pages = {79-91},
title = {The topological complexity of sets of convex differentiable functions.},
url = {http://eudml.org/doc/44479},
volume = {11},
year = {1998},
}

TY - JOUR
AU - Yahdi, Mohammed
TI - The topological complexity of sets of convex differentiable functions.
JO - Revista Matemática Complutense
PY - 1998
VL - 11
IS - 1
SP - 79
EP - 91
AB - 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.
LA - eng
KW - Funciones continuas; Funciones convexas; Espacios de Banach; Espacios de Frechet; Funciones diferenciables; topology of uniform convergence on bounded subsets; Polish space; analytic subset; Gâteaux differentiable; Fréchet-differentiable
UR - http://eudml.org/doc/44479
ER -