Higher connectedness properties of support points and functionals of convex sets

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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.
Original languageEnglish
Pages (from-to)1236-1254
Number of pages19
JournalCANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
Volume65
DOIs
Publication statusPublished - 2013

Keywords

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

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