Nonexistence of linear operators extending Lipschitz (pseudo)metrics

DOI10.5486/PMD.2012.4913zbMATH Open1265.26008arXiv1207.2952OpenAlexW3102981606MaRDI QIDQ2915417

Mykhailo Zarichnyi, Dušan Repovš

Publication date: 17 September 2012

Published in: Publicationes Mathematicae Debrecen (Search for Journal in Brave)

Abstract: We present an example of a zero-dimensional compact metric space $X$ and its closed subspace $A$ such that there is no continuous linear extension operator for the Lipschitz pseudometrics on $A$ to the Lipschitz pseudometrics on $X$. The construction is based on results of A. Brudnyi and Yu. Brudnyi concerning linear extension operators for Lipschitz functions.

Full work available at URL: https://arxiv.org/abs/1207.2952

zbMATH Keywords

extension operatorLipschitz functionbi-Lipschitz equivalencezero-dimensional compactumLipschitz pseudometric

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Lipschitz (Hölder) classes (26A16) Special maps on metric spaces (54E40) Extension of maps (54C20)

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