Algebraic approximation of germs of real analytic sets
Marco Ferrarotti, Elisabetta Fortuna, L. Wilson · Proceedings of the American Mathematical Society · 2010
Two subanalytic subsets of R n \mathbb {R}^n are s s -equivalent at a common point, say O O , if the Hausdorff distance between their intersections with the sphere centered at O O of radius r r goes to zero faster than r s r^s . In the present paper we investigate the existence of an algebraic representative in every s s -equivalence class of subanalytic sets. First we prove that such a result holds for the zero-set V ( f ) V(f) of an analytic map f f when the regular points of f f are dense in V ( f ) V(f) . Moreover we present some results concerning the algebraic approximation of the image of a real analytic map f f under the hypothesis that f − 1 ( O ) = { O } f^{-1}(O)=\{O\} .