Covering a Banach space

Vladimir P. Fonf, Clemente Zanco

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

A well-known theorem by H. Corson states that if a Banach space admits a locally finite covering by bounded closed convex subsets, then it contains no infinite-dimensional reflexive subspace. We strengthen this result proving that if an infinite-dimensional Banach space admits a locally finite covering by bounded ω-closed subsets, then it is c0-saturated, thus answering a question posed by V. Klee concerning locally finite coverings of l1 spaces. Moreover, we provide information about massiveness of the set of singular points in (PC) spaces.

Original languageEnglish
Pages (from-to)2607-2611
Number of pages5
JournalProceedings of the American Mathematical Society
Volume134
Issue number9
DOIs
StatePublished - 1 Sep 2006

Keywords

  • (PC) property
  • Covering
  • Locally finite covering
  • Space c

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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