Archivio Istituzionale della RicercaAbstract. Two subanalytic subsets of Rn are called s-equivalent at a common point P if the Hausdorff distance between their intersections with the sphere centered at P of radius r vanishes to order > s when r tends to 0. In this paper we prove that every s-equivalence class of a closed semianalytic set contains a semialgebraic representative of the same dimension. In other words any semianalytic set can be locally approximated of any order s by means of a semialgebraic set and hence, by previous results, also by means of an algebraic one.
Local algebraic approximation of semianalytic sets / Ferrarotti, Massimo; Fortuna, E.; Wilson, L.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 1088-6826. - STAMPA. - 143:1(2015), pp. 13-23. [10.1090/S0002-9939-2014-12212-X]
Local algebraic approximation of semianalytic sets
FERRAROTTI, Massimo;
2015
Abstract
Abstract. Two subanalytic subsets of Rn are called s-equivalent at a common point P if the Hausdorff distance between their intersections with the sphere centered at P of radius r vanishes to order > s when r tends to 0. In this paper we prove that every s-equivalence class of a closed semianalytic set contains a semialgebraic representative of the same dimension. In other words any semianalytic set can be locally approximated of any order s by means of a semialgebraic set and hence, by previous results, also by means of an algebraic one.
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https://hdl.handle.net/11583/2505562
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