Local algebraic approximation of semianalytic sets
| Autor: | Massimo Ferrarotti, Leslie Wilson, Elisabetta Fortuna |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Semialgebraic set
Discrete mathematics Class (set theory) Applied Mathematics General Mathematics Dimension (graph theory) Order (ring theory) Geometric Topology (math.GT) Astrophysics::Cosmology and Extragalactic Astrophysics Radius 14P15 32B20 32S05 (Primary) Set (abstract data type) Mathematics - Algebraic Geometry Mathematics - Geometric Topology Hausdorff distance FOS: Mathematics Algebraic number Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Proceedings of the American Mathematical Society. 143:13-23 |
| ISSN: | 1088-6826 0002-9939 |
| Popis: | 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). Comment: 10 pages, 0 figures, amslatex |
| Databáze: | OpenAIRE |
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