Properties of the Holmes space

The following properties of the Holmes space H are established:(i) the Metric Approximation Property (MAP). ∗ -closure of the set of extreme points of the unit ball B H ∗ of the dual space H ∗ is the whole ball B H ∗ . ly of compact subsets X ⊂ U of the Urysohn space is described such that the Lipschitz-free space F ( X ) has a finite-dimensional decomposition and is not complemented in H.