Nash Manifolds and Schwartz Functions on Them
نویسنده
چکیده
These are the lecture notes for my talk on December 1, 2014 at the BIRS workshop “Motivic Integration, Orbital Integrals, and Zeta-Functions”. 1. Semi-algebraic sets and the Seidenberg-Tarski theorem In this section we follow [BCR]. Definition 1.1. A subset A ⊂ R is called a semi-algebraic set if it can be presented as a finite union of sets defined by a finite number of polynomial equalities and inequalities. In other words, if there exist finitely many polynomials fij , gik ∈ R[x1, ..., xn] such that
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