Nonexistence of linear operators extending Lipschitz (pseudo)metric
  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. 
Du\v{s}an Repov\v{s} and Mykhailo Zarichnyi
math.GN math.MG