Algebraic Approximation of Germs of Real Analytic Sets

Two subanalytic subsets of Rn are s-equivalent at a common point, say O, if the Hausdorff distance between their intersections with the sphere centered at O of radius r goes to zero faster than rs. In the present paper we investigate the existence of an algebraic representative in every sequivalence class of subanalytic sets. First we prove that such a result holds for the zero-set V (f) of an analytic map f when the regular points of f are dense in V (f). Moreover we present some results concerning the algebraic approximation of the image of a real analytic map f under the hypothesis that f−1(O) = {O}.