A novel construction of Urysohn universal ultrametric space via the Gromov-Hausdorff ultrametric

2020/07/16 by Wan, Zhengchao
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2007.08105

Abstract

We establish universality and ultra-homogeneity of (U,u_GH), the collection of all compact ultrametric spaces endowed with the so-called Gromov-Hausdorff ultrametric. This result also gives rise to a novel construction of the so-called R-Uryoshn universal ultrametric space for each countable subset R⊂ℝ_{≥ 0} containing 0.

Related

• Constructions of Urysohn universal ultrametric spaces
• Uniqueness and homogeneity of non-separable Urysohn universal ultrametric spaces
• Characterizations of Urysohn universal ultrametric spaces
• Gromov-Hausdorff ultrametric
• The ultrametric Gromov-Wasserstein distance