Covering the unit sphere of certain banach spaces by sequences of slices and balls

Vladimir P. Fonf, Clemente Zanco

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We prove that, given any covering of any infinite-dimensional Hilbert space H by countably many closed balls, some point exists in H which belongs to infinitely many balls. We do that by characterizing isomorphically polyhedral separable Banach spaces as those whose unit sphere admits a point-finite covering by the union of countably many slices of the unit ball.

Original languageEnglish
Pages (from-to)42-50
Number of pages9
JournalCanadian Mathematical Bulletin
Volume57
Issue number1
DOIs
StatePublished - 1 Mar 2014

Keywords

  • Hilbert spaces
  • Point finite coverings
  • Polyhedral spaces
  • Slices

ASJC Scopus subject areas

  • Mathematics (all)

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