On strong \(C^ 0\)-equivalence of real analytic functions
type: Item
instance of: scholarly article
title: On strong \(C^ 0\)-equivalence of real analytic functions
zbMATH Open document ID: 0788.32024
author: Satoshi Koike
published in: Journal of the Mathematical Society of Japan
publication date: 1993-12-20T00:00:00Z
review text: The author introduces the notion of strong \(C^ 0\)-equivalence for real analytic germs \((\mathbb{R}^ n,0) \to(\mathbb{R},0)\) which is the usual \(C^ 0\)- equivalence preserving the tangency of analytic arcs at the origin \(0 \in \mathbb{R}^ n\). Then he considers two \(\mu\)-constant one-parameter families of complex polynomial germs \[ x^{15}+xy^ 7+z^ 5+ty^ 6z,\;x^ 8+y^{16}+z^{16}+x^ 3yz^ 3+tx^ 5z^ 2, \] constructed by \textit{J. Briançon} and \textit{J.-P. Speder} [C. R. Acad. Sci, Paris, Ser. A 280, 365-367 (1975; Zbl 0331.32010)] and \textit{M. Oka} [Contemp. Math. 90, 199- 210 (1989; Zbl 0682.32011)] respectively. Both families have a weak simultaneous resolution but have no strong simultaneous resolution. However, the author proves that in the real case these families are topologically trivial but not strongly \(C^ 0\)-trivial.
Mathematics Subject Classification ID: 32S15
Mathematics Subject Classification ID: 26E05
Mathematics Subject Classification ID: 57R45
zbMATH DE Number: 469064
zbMATH Keywords: analytic equivalence
zbMATH Keywords: \(\mu\)-constant family
zbMATH Keywords: topological triviality
zbMATH Keywords: simultaneous resolution
reviewed by: Aleksandr G. Aleksandrov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04520313
OpenAlex ID: W2144779730
DOI: 10.2969/JMSJ/04520313
description: scientific article; zbMATH DE number 469064