Approximation of definable sets by compact families, and upper bounds on homotopy and homology
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.
Date of this Version
Gabrielov, Andrei and Vorobjov, Nicolai, "Approximation of definable sets by compact families, and upper bounds on homotopy and homology" (2009). Department of Earth, Atmospheric, and Planetary Sciences Faculty Publications. Paper 111.
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