Complements of subanalytic sets and existential formulas for analytic functions
type: Item
instance of: scholarly article
title: Complements of subanalytic sets and existential formulas for analytic functions
zbMATH Open document ID: 0851.32009
published in: Inventiones Mathematicae
publication date: 1996-06-09T00:00:00Z
review text: The author is the same person who started, even before Hironaka, the theory of subanalytic sets in 1968 [the author, Funct. Anal. Appl. 2, 282-291 (1968); translation from Funkts. Anal. Prilozh. 2, No. 4, 18-30 (1968; Zbl 0179.08503)]. In the cited paper he proved, among other things, the essential result: the complement of a subanalytic set in \(\mathbb{R}^n\) is subanalytic. Now he proves the same result for the subanalytic sets described by a subalgebra of analytic functions, closed under differentiation. The translation into the logic is given, too. Needless to say, such a result is not easy to obtain and the author uses the newest developments (like \textit{A. G. Khovanskij} [`Fewnomials' (1991; Zbl 0728.12002)], for example). The paper is short and well written.
Mathematics Subject Classification ID: 32B20
zbMATH DE Number: 885518
zbMATH Keywords: subanalytic sets
author: Andrei Gabrielov
reviewed by: Zofia Denkowska
MaRDI profile type: Publication
full work available at URL: s002220050066
OpenAlex ID: W1997612982
DOI: 10.1007/S002220050066
description: scientific article; zbMATH DE number 885518