Properties and Morphisms of Finite Ultrametric Spaces and Their Representing Trees
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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.
Key wordsball-preserving mapping embedding of trees finite ultrametric space Gomory-Hu inequality representing tree strictly binary tree weighted graph
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