Finitely locally finite coverings of Banach spaces

Vladimir P. Fonf, Clemente Zanco

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

A well-known result due to H. Corson states that, for any covering τ by closed bounded convex subsets of any Banach space X containing an infinite-dimensional reflexive subspace, there exists a compact subset C of X that meets infinitely many members of τ. We strengthen this result proving that, even under the weaker assumption that X contains an infinite-dimensional separable dual space, an (algebraically) finite-dimensional compact set C with that property can always be found.

Original languageEnglish
Pages (from-to)640-650
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume350
Issue number2
DOIs
StatePublished - 15 Feb 2009

Keywords

  • Covering
  • Finitely locally finite covering
  • Locally finite covering

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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