# The topological complexity of sets of convex differentiable functions.

Revista Matemática Complutense (1998)

- Volume: 11, Issue: 1, page 79-91
- ISSN: 1139-1138

## Access Full Article

top## Abstract

top## How to cite

topYahdi, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.