Critical sets in 3-space
type: Item
instance of: scholarly article
title: Critical sets in 3-space
zbMATH Open document ID: 0796.58012
DOI: 10.1007/BF02699187
published in: Publications Mathématiques
publication date: 1994-03-07T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/104088
review text: The paper is devoted to the problem when a nonempty compact set \(C\) in \(\mathbb{R}^ 3\) is the set of critical points for a proper, smooth function on \(\mathbb{R}^ 3\). It is proved that this is true if \(C\) is Antoine's necklace in \(\mathbb{R}^ 3\). In addition one establishes that any tame link in \(\mathbb{R}^ 3\) is the set of critical points for some smooth functions but generally not for a proper function.
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 57R70
zbMATH DE Number: 508544
zbMATH Keywords: flow
zbMATH Keywords: critical points
zbMATH Keywords: link
author: Matthew A. Grayson
author: Charles Pugh
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 508544