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

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-Urysohn universal ultrametric space for each countable subset R ⊂ R ≥ 0 containing 0.