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24 June 2024
  » arxiv » 2302.00306

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Uniqueness and homogeneity of non-separable Urysohn universal ultrametric spaces
Yoshito Ishiki ;
Date 1 Feb 2023
AbstractUrysohn constructed an universal metric space, which is today called the Urysohn universal metric space. Some authors recently investigate an ultrametric analogue of this space, which is also our main subject in this paper. We first introduce a petaloid ultrametric space, which is intended to be a standard class of non-separable Urysohn universal ultrametric spaces. Next we prove that all petaloid spaces are isometric to each other and homogeneous for all finite subspaces. As an application, we show that the following spaces are petaloid, and hence they are isometric to each other and homogeneous for finite subspaces: (1) The space of all continuous functions from the Cantor space into the space of non-negative real numbers equipped with near-discrete topology, (2) the space of all continuous ultrametrics on a zero-dimensional infinite compact metrizable space, and (3) the non-Archimedean Gromov--Hausdorff space.
Source arXiv, 2302.00306
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