Geodesic
Higher Connectedness Properties of Support Points and Functionals of Convex Sets
Canadian journal of mathematics, Tome 65 (2013) no. 6, pp. 1236-1254

Voir la notice de l'article provenant de la source Cambridge

DOI

We prove that the set of all support points of a nonempty closed convex bounded set $C$ in a real infinite-dimensional Banach space $X$ is $\text{AR}$ ( $\sigma $ -compact) and contractible. Under suitable conditions, similar results are proved also for the set of all support functionals of $C$ and for the domain, the graph, and the range of the subdifferential map of a proper convex lower semicontinuous function on $X$ .
DOI : 10.4153/CJM-2012-048-8
Mots-clés : 46A55, 46B99, 52A07, convex set, support point, support functional, absolute retract, Leray-Schauder continuation principle 
Bernardi, Carlo Alberto De. Higher Connectedness Properties of Support Points and Functionals of Convex Sets. Canadian journal of mathematics, Tome 65 (2013) no. 6, pp. 1236-1254. doi: 10.4153/CJM-2012-048-8
@article{10_4153_CJM_2012_048_8,
     author = {Bernardi, Carlo Alberto De},
     title = {Higher {Connectedness} {Properties} of {Support} {Points} and {Functionals} of {Convex} {Sets}},
     journal = {Canadian journal of mathematics},
     pages = {1236--1254},
     year = {2013},
     volume = {65},
     number = {6},
     doi = {10.4153/CJM-2012-048-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-048-8/}
}
TY  - JOUR
AU  - Bernardi, Carlo Alberto De
TI  - Higher Connectedness Properties of Support Points and Functionals of Convex Sets
JO  - Canadian journal of mathematics
PY  - 2013
SP  - 1236
EP  - 1254
VL  - 65
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-048-8/
DO  - 10.4153/CJM-2012-048-8
ID  - 10_4153_CJM_2012_048_8
ER  - 
%0 Journal Article
%A Bernardi, Carlo Alberto De
%T Higher Connectedness Properties of Support Points and Functionals of Convex Sets
%J Canadian journal of mathematics
%D 2013
%P 1236-1254
%V 65
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-048-8/
%R 10.4153/CJM-2012-048-8
%F 10_4153_CJM_2012_048_8

Cité par Sources :