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

摘要

We establish universality and ultra-homogeneity of (u, u(GH) ), the collection of all compact ultrametric spaces endowed with the so-called Grormov-Hausdorff ultrametric. This result also gives rise to a novel construction of the so-called R-Urysohn universal ultrametric space for each countable subset R subset of R0 containing 0. (C) 2021 Elsevier B.V. All rights reserved.