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Properties and Morphisms of Finite Ultrametric Spaces and Their Representing Trees

  • Oleksiy DovgosheyEmail author
  • Evgeniy Petrov
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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: YZ for all nonempty YX and ZY.

Key words

ball-preserving mapping embedding of trees finite ultrametric space Gomory-Hu inequality representing tree strictly binary tree weighted graph 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Function Theory DepartmentInstitute of Applied Mathematics and Mechanics of NASUSlovyanskUkraine

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