Properties and Morphisms of Finite Ultrametric Spaces and Their Representing Trees

Аннотация

The present paper is a brief survey of properties of finite ultrametric spaces X and corresponding properties of the representing trees T_X obtained by authors over the last six years. Some new results are also presented. In particular, a structural characteristic of the representing trees T_X is found for the finite ultrametric spacesX which admit a ball-preserving mapping f: Y → Z for all nonempty Y ⊆ X and Z ⊆ Y.