Local algebraic approximation of semianalytic sets
Algebraic Geometry
2012-09-17 v1 Geometric Topology
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 of order greater than 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 (so long as the semianalytic set has codimension at least 1).
Cite
@article{arxiv.1209.3123,
title = {Local algebraic approximation of semianalytic sets},
author = {Massimo Ferrarotti and Elisabetta Fortuna and Leslie Wilson},
journal= {arXiv preprint arXiv:1209.3123},
year = {2012}
}
Comments
10 pages, 0 figures, amslatex