Approximation of Definable Sets by Compact Families, and Upper Bounds on Homotopy and Homology
نویسنده
چکیده
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.
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