Acta Mathematica Vietnamica
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STRATIFICATION OF FAMILIES OF FUNCTIONS DEFINABLE IN O-MINIMAL STRUCTURES
TA LÊ LOIpp. 239-244
Abstract
We prove the existence of Thom stratifications for families of functions definable in any o-minimal structure. The theory of o-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 $\mathbb R^n$ with bounded degree.