Properties of the Holmes space

The following properties of the Holmes space H are established:(i)H has the Metric Approximation Property (MAP).(ii)The w∗-closure of the set of extreme points of the unit ball BH∗ of the dual space H∗ is the whole ball BH∗.A family 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.