The Kuo condition, an inequality of Thom's type and \((c)\)-regularity
type: Item
instance of: scholarly article
title: The Kuo condition, an inequality of Thom's type and \((c)\)-regularity
zbMATH Open document ID: 0894.58005
DOI: 10.1016/S0040-9383(97)00020-7
published in: Topology
publication date: 1998-09-07T00:00:00Z
review text: In [\textit{K. Bekka}, Lect. Notes Math. 1462, 42-62 (1991; Zbl 0733.58003)] the first author introduced the notion of \((c)\)-regularity which is weaker than Whitney \((b)\)-regularity, and he showed that the \((c)\)-regularity condition implies topological triviality. In this paper, the authors give a characterization of \((c)\)-regularity (Theorem 2.4). Using it, they can show that the Kuo condition (given in Theorem 1.4) implies the \((c)\)-regularity condition (Theorems 2.7, 2.8). A different proof of the Trotman-Wilson result is also given (Corollary 2.9). Apart from this, the authors show that a particular Thom-type inequality is equivalent to another type of inequality (Theorem 2.14). Using this result, they show that the Thom condition in Theorem 1.3 is equivalent to the Kuiper-Kuo condition in the function case (Corollary 2.16). As another corollary of this, a result on Fukuda's ideal is obtained.
Mathematics Subject Classification ID: 58A20
zbMATH DE Number: 1089983
zbMATH Keywords: \((c)\)-regularity
zbMATH Keywords: Kuo condition
zbMATH Keywords: Thom condition
author: Karim Bekka
author: Satoshi Koike
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1089983