1. Roundness properties of ultrametric spaces
- Author
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Katelynn Kochalski, Elizabeth Wesson, Anthony Weston, Timothy Faver, Heidi Verheggen, and Mathav Murugan
- Subjects
Discrete mathematics ,Euclidean space ,54E40, 46C05, 51K05 ,General Mathematics ,General Topology (math.GN) ,Type (model theory) ,Condensed Matter::Disordered Systems and Neural Networks ,Roundness (object) ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,Metric space ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,FOS: Mathematics ,Mathematics::Metric Geometry ,Point (geometry) ,Classical theorem ,Ultrametric space ,Mathematics ,Mathematics - General Topology - 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., 12 pages
- Published
- 2012