Almost flat locally finite coverings of the sphere

V. P. Fonf, C. Zanco

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


For any subset A of the unit sphere of a Banach space X and for ε [0,2) the notion of ε-flatness is introduced as a "measure of non-flatness" of A. For any positive ε, construction of locally finite tilings of the unit sphere by ε-flat sets is carried out under suitable ε-renormings of X in a quite general context; moreover, a characterization of spaces having separable dual is provided in terms of the existence of such tilings. Finally, relationships between the possibility of getting such tilings of the unit sphere in the given norm and smoothness properties of the norm are discussed.

Original languageEnglish
Pages (from-to)269-281
Number of pages13
Issue number3
StatePublished - 1 Sep 2004


  • Duality mapping
  • Locally finite covering
  • ε-flat set

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • General Mathematics


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