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