Nonexistence of linear operators extending Lipschitz (pseudo)metrics (Q2915417)
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scientific article; zbMATH DE number 6083251
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonexistence of linear operators extending Lipschitz (pseudo)metrics |
scientific article; zbMATH DE number 6083251 |
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Nonexistence of linear operators extending Lipschitz (pseudo)metrics (English)
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17 September 2012
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Lipschitz pseudometric
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extension operator
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Lipschitz function
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zero-dimensional compactum
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bi-Lipschitz equivalence
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0.90604115
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0.8680974
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0.86349666
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0.8604417
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It is well-known that any Lipschitz pseudometric defined on a closed subset of a metric space admits an extension which is a Lipschitz pseudometric defined on the whole space. The authors consider the problem of existence of linear extension operators for Lipschitz pseudometric. They show that there exist a zero-dimensional compact metric space \(X\) and its closed subspace \(A\) such that there is no continuous linear extension operator from the Lipschitz pseudometrics on \(A\) to the Lipschitz pseudometrics on \(X\). The construction is based on results of \textit{A. Brudnyi and Yu. Brudnyi} [Am. J. Math. 129, No. 1, 217--314 (2007; Zbl 1162.46042)] concerning the linear extension operators for Lipschitz functions.
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