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We study star-finite coverings of infinite-dimensional normed spaces. A family of sets is called star-finite if each of its members intersects only finitely many other members of the family. It follows from our results that an LUR or a uniformly Fréchet smooth infinite-dimensional Banach space does not admit star-finite coverings by closed balls. On the other hand, we present a quite involved construction of a star-finite covering of c0(Γ) by Fréchet smooth centrally symmetric bounded convex bodies. A similar but simpler construction shows that every normed space of countable dimension (and hence incomplete) has a star-finite covering by closed balls.
Lingua originaleEnglish
pagine (da-a)124384-N/A
RivistaJournal of Mathematical Analysis and Applications
Stato di pubblicazionePubblicato - 2020


  • Covering of normed space
  • Fréchet smooth body
  • Locally uniformly rotund norm


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