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24 June 2024
  » arxiv » 2302.00305

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Constructions of Urysohn universal ultrametric spaces
Yoshito Ishiki ;
Date 1 Feb 2023
AbstractIn this paper, we give new constructions of Urysohn universal ultrametric spaces. We first characterize a Urysohn universal ultrametric subspace of the space of continuous functions from a zero-dimensional compact Hausdorff space without isolated pints 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 analogue of Banach--Mazur theorem. Moreover, we prove that the space of 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 an analogue of Wan’s construction of Urysohn universal ultrametric space via the Gromov--Hausdorff ultrametric space.
Source arXiv, 2302.00305
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