Finite Ultrametric Balls

2018/10/07 by O. Dovgoshey, Dovgoshey, O. · 2 citations
Mathematics · #54E35 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:54E35

paper · pdf · doi:10.48550/arxiv.1810.03128

22 pages, 2 figures

arxiv created 2019/03/23 · arxiv updated 2019/03/26

Abstract

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.

Cited by

• Hausdorff distance between ultrametric balls
• Center of distances of ultrametric spaces generated by labeled trees

Related

• Totally bounded ultrametric spaces and locally finite trees
• Locally finite ultrametric spaces and labeled trees
• Ball-preserving mappings of finite ultrametric spaces
• Extremal properties and morphisms of finite ultrametric spaces and their representing trees
• Hausdorff distance between ultrametric balls