Approximation theorem and Hopf spaces (Q2732313)
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scientific article; zbMATH DE number 1623558
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation theorem and Hopf spaces |
scientific article; zbMATH DE number 1623558 |
Statements
18 June 2002
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Hopf space
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compact map
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approximation
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continuous map
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fixed point
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\(ANR(m)\) property
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homotopy
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Approximation theorem and Hopf spaces (English)
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The following is the main result of the paper. Let \(X\) be a normed vector space and \(f:D \to C\), a compact map; here, \(C\) is a (nonempty) closed part of \(X\) which is both \(ANR(m)\) and Hopf space, and \(D\) is some partof \(X\) with \(C\subseteq D\). Then, for each \(\varepsilon > 0\), there exists a continuous map \(h:D \to C\) which \(\varepsilon\)-approximates \(f\) and has a finite number of fixed points. Some direct applications of this fact are also discussed.
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