A counterexample to infinite-dimensional version of the Morse-Sard theorem (Q1812219)
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scientific article; zbMATH DE number 1931540
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A counterexample to infinite-dimensional version of the Morse-Sard theorem |
scientific article; zbMATH DE number 1931540 |
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A counterexample to infinite-dimensional version of the Morse-Sard theorem (English)
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13 October 2003
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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.
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Hausdorff measure
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rank
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Fréchet differentiability
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Morse critical points
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