Nonexistence of linear operators extending Lipschitz (pseudo)metric
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2012
- DOI:
- 10.48550/arXiv.1207.2952
- arXiv:
- arXiv:1207.2952
- Bibcode:
- 2012arXiv1207.2952R
- Keywords:
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- Mathematics - General Topology;
- Mathematics - Metric Geometry;
- 26A16;
- 54C20;
- 54E35;
- 54E40
- E-Print:
- arXiv admin note: substantial text overlap with arXiv:math/0408200