Any compact differentiable submanifold of \({\mathbb{R}}^ n\) has an algebraic approximation in \({\mathbb{R}}^ n\) (Q1114972)
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scientific article; zbMATH DE number 4086556
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Any compact differentiable submanifold of \({\mathbb{R}}^ n\) has an algebraic approximation in \({\mathbb{R}}^ n\) |
scientific article; zbMATH DE number 4086556 |
Statements
Any compact differentiable submanifold of \({\mathbb{R}}^ n\) has an algebraic approximation in \({\mathbb{R}}^ n\) (English)
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1988
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The author claims to have proven that any compact smooth submanifold of \({\mathbb{R}}^ n\) is isotopic to a nonsingular real gebraic set. Although this may turn out to be true, the proof given has several gaps. More precisely, examples can be constructed for which the function h in the proof cannot have the properties demanded of it.
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smooth submanifold of \({\mathbb{R}}^ n\)
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isotopic to a nonsingular real gebraic set
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