Homogeneity Properties of Some l1-Spaces

Let M be a family of subspaces of a metric space X. The space X is M–homogeneous if any isometry between two subspaces in M can be extended to an isometry of X. In the case when M is the family of all subspaces of X, the space X is said to be fully homogeneous. We show that the space L, where L is a fully homogeneous subspace of R, is R– homogeneous where R is the family of subspaces that are products of subsets of L. It is also shown that the space P0(Z) of all finite subsets of a set Z is WG–homogeneous where WG is the set of all well graded families of finite subsets of Z.