Higher connectedness properties of support points and functionals of convex sets

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer 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 originaleEnglish
pagine (da-a)1236-1254
Numero di pagine19
RivistaCANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
Volume65
DOI
Stato di pubblicazionePubblicato - 2013

Keywords

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

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