Roundness properties of ultrametric spaces

2012/01/31 by Timothy E. Faver, Katelynn Kochalski, Faver, Timothy +9
Mathematics · #46C05 #51K05 #54E40 #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.1201.6669

openalex publication_date 2012/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain several new characterizations of ultrametric spaces in terms of roundness, generalized roundness, strict p-negative type, and p-polygonal equalities (p > 0). This allows new insight into the isometric embedding of ultrametric spaces into Euclidean spaces. We also consider roundness properties additive metric spaces which are not ultrametric.

Citations

• Metric spaces and positive definite functions

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