Ensembles semi-algébriques symétriques par arcs. (Semi-algebraic sets symmetric by arcs)
type: Item
instance of: scholarly article
title: Ensembles semi-algébriques symétriques par arcs. (Semi-algebraic sets symmetric by arcs)
zbMATH Open document ID: 0686.14027
DOI: 10.1007/BF01460044
author: Krzysztof Kurdyka
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164472
review text: The author defines and studies a natural and interesting class of semi- algebraic sets, that is, the class of semi-algebraic sets symmetric by arcs. A semi-algebraic set E in \({\mathbb{R}}^ n\) is called \textit{symmetric by arcs} if, for any analytic arc \(\gamma:\quad (-1,1)\to {\mathbb{R}}^ n,\) \(\gamma\) ((-1,0))\(\subset E\) implies \(\gamma\) ((-1,1))\(\subset E\). Then, define AR-topology of \({\mathbb{R}}^ n\) such that \(E\subset {\mathbb{R}}^ n\) is closed if and only if E is a semi-algebraic set symmetric by arcs. In this paper, for example, it is given a characterization of connected components of desingularization of an algebraic set, in the ward of AR- irreducible decomposition. - Further, the author defines the notion of arc-analytic mapping and he studies, for a semi-algebraic set X symmetric by arcs, the structure of the ring \(A_ a(X)\) of functions \(X\to {\mathbb{R}}\) semi-algebraic and arc-analytic.
Mathematics Subject Classification ID: 14Pxx
Mathematics Subject Classification ID: 58A07
Mathematics Subject Classification ID: 14E15
zbMATH DE Number: 4123883
zbMATH Keywords: Nash function
zbMATH Keywords: semi-algebraic sets symmetric by arcs
zbMATH Keywords: desingularization
zbMATH Keywords: arc-analytic mapping
reviewed by: Goo Ishikawa
MaRDI profile type: Publication
cites work: Q4143433
cites work: Resolution of singularities of an algebraic variety over a field of characteristic zero. I
cites work: Surjectivity of certain injective semialgebraic transformations of \({\mathbb{R}}\) n
cites work: Q5651510
cites work: Q5566770
cites work: Real algebraic manifolds
cites work: Q3693813
cites work: Sur l'anneau des fonctions de Nash globales
cites work: Q5799167
cites work: Studies in Equisingularity II. Equisingularity in Codimension 1 (and Characteristic Zero)
OpenAlex ID: W2912924585
description: scientific article; zbMATH DE number 4123883