ROUNDNESS PROPERTIES OF ULTRAMETRIC SPACES

DOI10.1017/S0017089513000438zbMath1311.46020arXiv1201.6669OpenAlexW2089901684MaRDI QIDQ2921056

Katelynn D. Kochalski, Heidi Verheggen, Anthony Weston, Elizabeth Wesson, Mathav Kishore Murugan, Timothy E. Faver

Publication date: 30 September 2014

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.6669

zbMATH Keywords

isometryultrametricgeneralized roundnessstrict negative typeadditive metricleaf metric

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Distance in graphs (05C12) Special maps on metric spaces (54E40) General theory of distance geometry (51K05) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85) Geometric embeddings of metric spaces (30L05)

Related Items (7)

Roundness properties of Banach spaces ⋮ Asymptotic negative type properties of finite ultrametric spaces ⋮ Estimating the gap of finite metric spaces of strict \(p\)-negative type ⋮ COMPARING THE GENERALISED ROUNDNESS OF METRIC SPACES ⋮ The maximal generalised roundness of finite metric spaces ⋮ Embeddability of snowflaked metrics with applications to the nonlinear geometry of the spaces \(L_p\) and \(\ell_p\) for \(0<p<\infty\) ⋮ Polygonal equalities and virtual degeneracy in \(L_p\)-spaces

Cites Work

• Trees, ultrametrics, and noncommutative geometry
• Metric trees of generalized roundness one
• On the supremal \(p\)-negative type of finite metric spaces
• On the gap of finite metric spaces of \(p\)-negative type
• Strict \(p\)-negative type of a metric space
• Enhanced negative type for finite metric trees
• Edge lengths guaranteed to form a simplex
• Generalized roundness and negative type
• Finite metric spaces of strictly negative type
• Low dimensional embeddings of ultrametrics.
• A note on the metric properties of trees
• Trees and ultrametric spaces: A categorical equivalence
• Isometric embedding of finite ultrametric spaces in Banach spaces
• On the generalized roundness of finite metric spaces
• The classification of metrics and multivariate statistical analysis
• Roundness properties of groups.
• On the nonexistence of uniform homeomorphisms between \(L^ p\)-spaces
• On a problem of Smirnov
• Uniform structures and square roots in topological groups. I
• Uniform structures and square roots in topological groups. II
• Remarks to Maurice Frechet's article ``Sur la definition axiomatique d'une classe d'espaces vectoriels distancies applicables vectoriellement sur l'espace de Hilbert
• On certain metric spaces arising from euclidean spaces by a change of metric and their imbedding in Hilbert space
• Hyperbolic spaces are of strictly negative type
• Distance geometry in quasihypermetric spaces. III
• Pictures of Ultrametric Spaces, the p-Adic Numbers, and Valued Fields
• A Review of Hierarchical Classification
• Scaled Enflo type is equivalent to Rademacher type

This page was built for publication: ROUNDNESS PROPERTIES OF ULTRAMETRIC SPACES