An embedding, an extension, and an interpolation of ultrametrics

2020/08/24 by Yoshito Ishiki, Ishiki, Yoshito · 1 citation
Mathematics · #54E52 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #Primary 54E35 #Secondary 30L05

paper · pdf · doi:10.48550/arxiv.2008.10209

openalex publication_date 2020/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A simple proof of Hausdorff's theorem on extending metrics
• Embedding proper ultrametric spaces into ℓ_p and its application to nonlinear Dvoretzky's theorem

Cited by

• Forbidden Four Cycle, Star Graphs and Isometric Embeddings

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