An embedding, an extension, and an interpolation of ultrametrics

Abstract

The notion of the ultrametrics can be considered as a zero-dimensional analogue of ordinary metrics, and it is expected to prove ultrametric versions of theorems on metric spaces. In this paper, we provide ultrametric versions of the Arens--Eells isometric embedding theorem of metric spaces, the Hausdorff extension theorem of metrics, the Niemytzki--Tychonoff characterization theorem of the compactness, and the author's interpolation theorem of metrics and theorems on dense subsets of spaces of metrics.

To appear in p-Adic Numbers, Ultrametric Analysis and Applications

References in corpus (3)

• On the Assouad dimension and convergence of metric spaces
• Embedding proper ultrametric spaces into ${\ell }_p$ and its application to nonlinear Dvoretzky's theorem
• A novel construction of Urysohn universal ultrametric space via the Gromov-Hausdorff ultrametric