Semi-analyticité et sous-analyticité. (Semi-analyticity and sub- analyticity)
type: Item
instance of: scholarly article
title: Semi-analyticité et sous-analyticité. (Semi-analyticity and sub- analyticity)
zbMATH Open document ID: 0601.32008
DOI: 10.1007/BF01769224
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1986-01-01T00:00:00Z
review text: Given a subanalytic set D, its subsets \(D_{ns}\) and \(D_{nN}\) are considered, defined as follows: \[ D_{ns}=\{x\in D: \text{ the germ \(D_ x\) is not semi-analytic}\}, \] \[ D_{nN}=\{x\in D: \text{ the germ \(D_ x\) is not Nash subanalytic}\}. \] Nash subanalytic sets, introduced and studied by Bierstone, Milman and Schwarz as a very useful tool for some important problems of differential analysis (composition, division) may be defined as images of proper, analytic, regular in the sense of Gabrielov mappings (one of the equivalent definitions). In the paper the authors study the relations between \(D_{ns}\) and \(D_{nN}\) (for example: \(D_{ns}=D_{nN}\cup (\sin g D)_{nN})\) as well as the structure of these sets in connection with other questions. (The subanalyticity of \(D_{ns}\) and \(D_{nN}\) was proved later by Pawłucki, Kraków).
Mathematics Subject Classification ID: 32B20
zbMATH DE Number: 3969046
zbMATH Keywords: non-Nash points set
zbMATH Keywords: non semi-analytic points set
zbMATH Keywords: Nash subanalytic sets
author: Elisabetta Fortuna
author: Margherita Galbiati
reviewed by: Zofia Denkowska
MaRDI profile type: Publication
cites work: Composite differentiable functions
cites work: Relations among analytic functions. I
cites work: Continuous linear division and extension of \(C^\infty\) functions
cites work: Quelques résultats sur les ensembles Nash sous-analytiques
cites work: Q4050890
cites work: Q3659889
cites work: Subanalytic sets in the calculus of variation
full work available at URL: https://doi.org/10.1007/bf01769224
OpenAlex ID: W2331386950
description: scientific article; zbMATH DE number 3969046