Article

Nonexistence of linear operators extending Lipschitz (pseudo)metric

07/2012; DOI:10.5486/PMD.2012.4913
Source: arXiv

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.

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