Approximation of definable sets by compact families, and upper bounds on homotopy and homology

A Gabrielov, Nicolai Vorobjov

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16 Citations (Scopus)


We prove new upper bounds on homotopy and homology groups of o-minimal sets in terms of their approximations by compact o-minimal sets. In particular, we improve the known upper bounds on Betti numbers of semialgebraic sets defined by quantifier-free formulae and obtain, for the first time, a singly exponential bound on Betti numbers of sub-Pfaffian sets.
Original languageEnglish
Pages (from-to)35-54
Number of pages20
JournalJournal of the London Mathematical Society
Issue number1
Early online date9 May 2009
Publication statusPublished - Aug 2009



  • betti numbers
  • pfaffian sets

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