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 s. 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}.

Algebraic approximation of germs of real analytic sets / Ferrarotti, Massimo; Fortuna, E.; Wilson, L.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 138:5(2010), pp. 1537-1548.

Algebraic approximation of germs of real analytic sets

Abstract

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 s. 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}.
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2010
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/2317463`
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