Nonexistence of linear operators extending Lipschitz (pseudo)metrics

Details Nonexistence of linear operators extending Lipschitz (pseudo)metrics Nonexistence of linear operators extending Lipschitz (pseudo)metrics

2004-08-15

arxiv.org/abs/math/0408200v1

Mathematics

General Topology

7 pages

Scientific paper

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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