On support points and support functionals of convex sets

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5 Citations (Scopus)

Abstract

Let K be a bounded closed convex subset of a real Banach space of dimension at least two. Then the set of the support points of K is pathwise connected and the set NA1(K) of the norm-one support functionals of K is uncountable in each nonempty open set that intersects the dual unit sphere. In particular, the set NA1(K) is always uncountable, which answers a question posed by L. Zajicek.
Original languageEnglish
Pages (from-to)15-27
Number of pages13
JournalIsrael Journal of Mathematics
Volume171
DOIs
Publication statusPublished - 2009

Keywords

  • Bishop-Phelps theorem
  • convex set
  • support functionals
  • support point

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