Higher Connectedness Properties of Support Points and Functionals of Convex Sets

Bernardi, Carlo Alberto De

Canadian journal of mathematics, Tome 65 (2013) no. 6, pp. 1236-1254

Résumé

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 $X$ .

Détail

DOI : 10.4153/CJM-2012-048-8

Mots-clés : 46A55, 46B99, 52A07, convex set, support point, support functional, absolute retract, Leray-Schauder continuation principle

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