Verdier and strict Thom stratifications in o-minimal structures
type: Item
instance of: scholarly article
title: Verdier and strict Thom stratifications in o-minimal structures
zbMATH Open document ID: 0909.32008
author: Ta Lê Loi
published in: Illinois Journal of Mathematics
publication date: 1998-10-28T00:00:00Z
review text: We prove the existence of Verdier stratifications for sets definable in any \(o\)-minimal structure on \((\mathbb{R},+, \cdot)\) [for the definition of \(o\)-minimal structures see \textit{L. van den Dries}, `Tame topology and \(O\)-minimal structures, Cambridge University Press (1997)]. It is also shown that the Verdier condition \((w)\) implies the Whitney condition (b) in \(o\)-minimal structures on \((\mathbb{R},+, \cdot)\). We establish the existence of \((w_f)\)-stratification of functions definable in polynomially bounded \(o\)-minimal structures [for the definition, see \textit{C. Miller}, Ann. Pure Appl. Logic 68, No. 1, 79-84 (1994; Zbl 0823.03018)].
Mathematics Subject Classification ID: 32S60
Mathematics Subject Classification ID: 14P10
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 1191166
zbMATH Keywords: strict Thom stratifications
zbMATH Keywords: \(o\)-minimal structures
zbMATH Keywords: Verdier stratifications
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1191166