Two subanalytic subsets of R^n 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 to 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
FORTUNA, ELISABETTA;
2015-01-01
Abstract
Two subanalytic subsets of R^n 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 to any order s by means of a semialgebraic set and hence, by previous results, also by means of an algebraic one.File in questo prodotto:
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