Higher connectedness properties of support points and functionals of convex sets

Carlo Alberto De Bernardi

doi:10.4153/CJM-2012-048-8

Higher connectedness properties of support points and functionals of convex sets

Carlo Alberto De Bernardi

Risultato della ricerca: Contributo in rivista › Articolo › peer review

Abstract

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 AR(sigma-compact) and contractible. Under suitable conditions, similar results are proved also for the set of all support functionals ofC and for the domain, the graph, and the range of the subdifferential map of a proper convex lower semicontinuous function on X.

Lingua originale	Inglese
pagine (da-a)	1236-1254
Numero di pagine	19
Rivista	CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
Volume	65
Numero di pubblicazione	6
DOI	https://doi.org/10.4153/CJM-2012-048-8
Stato di pubblicazione	Pubblicato - 2013

All Science Journal Classification (ASJC) codes

Matematica generale

Keywords

Absolute retract
Convex set
Leray-Schauder continuation principle
Mathematics (all)
Support functional
Support point

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10.4153/CJM-2012-048-8

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Higher connectedness properties of support points and functionals of convex sets

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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