Finite Ultrametric Balls

详细

The necessary and sufficient conditions under which a given family ℱ of subsets of finite set X coincides with the family B_X of all balls generated by some ultrametric d on X are found. It is shown that the representing tree of the ultrametric space (B_X, d_H) with the Hausdorff distance d_H can be obtained from the representing tree T_X of ultrametric space (X, d) by adding a leaf to every internal vertex of T_X.