A counterexample to infinite-dimensional version of the Morse-Sard theorem
type: Item
instance of: scholarly article
title: A counterexample to infinite-dimensional version of the Morse-Sard theorem
zbMATH Open document ID: 1030.58005
author: Haiyi Jiang
published in: Applied Mathematics. Series B (English Edition)
publication date: 2003-10-13T00:00:00Z
review text: The author establishes that the Morse criticality theorem can not be extended to infinite-dimensional Banach spaces. More precisely, an example is provided showing that there exists a smooth rank-1 real map \(j\) defined on \(l^2\) such that \(j(A)\) has nonempty interior, for some subset \(A\) of \(l^2\) of critical points with finite Hausdorff dimension.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 37C45
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1931540
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: rank
zbMATH Keywords: Fréchet differentiability
zbMATH Keywords: Morse critical points
MaRDI profile type: Publication
full work available at URL: s11766-003-0085-3
OpenAlex ID: W2318552798
Wikidata QID: Q124822464
cites work: The measure of the critical values of differentiable maps
cites work: Counterexample to the Morse-Sard Theorem in the Case of Infinite-Dimensional Manifolds
cites work: On smooth \(\text{rank}\)-1 mappings of Banach spaces onto the plane
cites work: On the image size of singular maps. II
cites work: Some new perspectives on Sard's theorem
cites work: Q3996401
cites work: Hausdorff Measure of Critical Images on Banach Manifolds
DOI: 10.1007/S11766-003-0085-3
description: scientific article; zbMATH DE number 1931540