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.
|Titolo:||Local algebraic approximation of semianalytic sets|
|Data di pubblicazione:||2015|
|Digital Object Identifier (DOI):||10.1090/S0002-9939-2014-12212-X|
|Appare nelle tipologie:||1.1 Articolo in rivista|