Nonexistence of linear operators extending Lipschitz (pseudo)metrics
Michael Zarichnyi
Abstract
We provide 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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