Any compact differentiable submanifold of \({\mathbb{R}}^ n\) has an algebraic approximation in \({\mathbb{R}}^ n\)
type: Item
instance of: scholarly article
title: Any compact differentiable submanifold of \({\mathbb{R}}^ n\) has an algebraic approximation in \({\mathbb{R}}^ n\)
zbMATH Open document ID: 0664.57010
DOI: 10.1016/0040-9383(88)90039-0
author: Alberto Tognoli
published in: Topology
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 57R12
Mathematics Subject Classification ID: 32C05
zbMATH DE Number: 4086556
zbMATH Keywords: smooth submanifold of \({\mathbb{R}}^ n\)
zbMATH Keywords: isotopic to a nonsingular real gebraic set
reviewed by: Henry C. King
MaRDI profile type: Publication
full work available at URL: 0040-9383(88)90039-0
OpenAlex ID: W2084247771
description: scientific article; zbMATH DE number 4086556