Stratification of Families of Functions definable in O minimal Structures

Ta Le Loi

Abstract

     We prove the existence of Thom stratifications for families of functions definable in any o-minimal structure. The theory of 0-minimal structures is a generalization of semi-algebraic and sub-analytic geometry. Our result implies Fukuda's Theorem on the finiteness of topological types for polynomials on Rn with boundeddegree.