Lipschitz mappings on the unit sphere of an infinite-dimensional normed space (Q1865240)
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scientific article; zbMATH DE number 1887593
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lipschitz mappings on the unit sphere of an infinite-dimensional normed space |
scientific article; zbMATH DE number 1887593 |
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Lipschitz mappings on the unit sphere of an infinite-dimensional normed space (English)
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25 March 2003
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Given an infinite-dimensional normed space \(X\) with unit sphere \(S(X)\), the authors prove that there exists a Lipschitz continuous map \(f:S(x)\to S(x)\) such that \(\inf\{\|f(x)\pm x\|:x\in S(x)\}>0\).
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existence
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Lipschitz continuous map
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