2023/02/01 by Ishiki, Yoshito · 2 citations
#FOS: Mathematics #General Topology (math.GN) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2302.00305
In this paper, we give new constructions of Urysohn universal ultrametric spaces. We first characterize a Urysohn universal ultrametric subspace of the space of all continuous functions whose images contain the zero, from a zero-dimensional compact Hausdorff space without isolated points into the space of non-negative real numbers equipped with the nearly discrete topology. As a consequence, the whole function space is Urysohn universal, which can be considered as a non-Archimedean analog of Banach--Mazur theorem. As a more application, we prove that the space of all continuous pseudo-ultrametrics on a zero-dimensional compact Hausdorff space with an accumulation point is a Urysohn universal ultrametric space. This result can be considered as a variant of Wan's construction of Urysohn universal ultrametric space via the Gromov--Hausdorff ultrametric space.