Nonexistence of linear operators extending Lipschitz (pseudo)metrics

作者：Repovs Dusan^*; Zarichnyi Michael

来源：Publicationes Mathematicae-Debrecen, 2012, 81(1-2): 31-39.

DOI：10.5486/PMD.2012.4913

• Lipschitz pseudometric
• extension operator
• Lipschitz function
• zero-dimensional compactum
• bi-Lipschitz equivalence

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.

• 出版日期2012-7