On metric properties of stratified sets
type: Item
instance of: scholarly article
title: On metric properties of stratified sets
zbMATH Open document ID: 1033.58005
author: Karim Bekka
author: David Trotman
published in: Manuscripta Mathematica
publication date: 2003-07-02T00:00:00Z
review text: Topological properties of Thom-Whitney stratified spaces have been much studied by several mathematicians. The first author [Lect. Notes Math. 1462, 42--62 (1991; Zbl 0733.58003)] showed that after replacing Whitney's condition (b) by a weaker condition, called (C)-regularity, one still obtains most of the topological properties of Whitney stratified spaces, e.g., existence of a Thom-Mather structure as an abstract stratified set defined by a system of control data, invariance by transverse intersection and continuous controlled extension of stratified vector fields. In the paper under review, the authors study the class of locally radial stratified spaces which are (C)-regular for standard control functions. A locally compact regular stratified space is locally homeomorphic to a cone on a regular stratified space. The volume is locally finite and in fact equivalent to that of a ball of the same dimension. Stokes' theorem for certain regular stratified spaces is proved. Finally, the weakly Whitney stratified spaces are described. This class is intermediate between the classical Whitney stratified spaces and locally radial (C)-regular spaces.
Mathematics Subject Classification ID: 58A35
Mathematics Subject Classification ID: 32S60
Mathematics Subject Classification ID: 58C35
Mathematics Subject Classification ID: 26B20
zbMATH DE Number: 1945297
zbMATH Keywords: Thom-Whitney stratified space
zbMATH Keywords: (C)-regularity
zbMATH Keywords: weakly Whitney stratified space.
zbMATH Keywords: Stokes theorem
reviewed by: Ion Mihai
MaRDI profile type: Publication
full work available at URL: s00229-003-0354-8
OpenAlex ID: W2004105613
DOI: 10.1007/S00229-003-0354-8
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description: scientific article; zbMATH DE number 1945297