On the image size of singular maps. II
type: Item
instance of: scholarly article
title: On the image size of singular maps. II
zbMATH Open document ID: 0801.58005
DOI: 10.1215/S0012-7094-92-06818-9
author: Sean M. Bates
published in: Duke Mathematical Journal
publication date: 1993-08-08T00:00:00Z
review text: The author presents some new refinements of the well-known Morse-Sard theorem: If \(f\in C^ k(\mathbb{R}^ n,\mathbb{R}^ m)\) and \(k\geq \max\{n- m+1,1\}\), then the image of the critical set of \(f\) has Lebesgue \(m\)- measure zero. The paper contains two sections: (1) singular mappings of finite-dimensional spaces; (2) critical images in Banach spaces. It is a nice continuation of the author's previous paper [Proc. Am. Math. Soc. 114, No. 3, 699-705 (1992; Zbl 0749.58011)].
reviewed by: Dorin Andrica
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 57R70
Mathematics Subject Classification ID: 58K99
Mathematics Subject Classification ID: 26B35
zbMATH DE Number: 179203
zbMATH Keywords: Morse-Sard theorem
zbMATH Keywords: critical set
zbMATH Keywords: singular mappings
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 179203