Geometric algebra for sets with betweenness relations

DOI10.1007/s13366-022-00648-wOpenAlexW4281608770MaRDI QIDQ6174568

Walter Wenzel, Juergen Jost

Publication date: 17 August 2023

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13366-022-00648-w

zbMATH Keywords

treeintervalgraphgeometric algebraHelly propertynormed vector spacebetweenness relationhyperconvex spacegate condition(complete) metric space(totally) ordered setabelian group with generators and relationsgeodesic -- in differential geometry and in graph theorytripod space

Mathematics Subject Classification ID

Partial orders, general (06A06) Trees (05C05) Complete metric spaces (54E50) Generators, relations, and presentations of groups (20F05) Metric spaces, metrizability (54E35) Distance in graphs (05C12) General theory of distance geometry (51K05) Curves in Euclidean and related spaces (53A04) General biology and biomathematics (92B05)

Cites Work

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• Geometric algebra for combinatorial geometries
• \(T\)-theory: An overview
• Topology and curvature of metric spaces
• Six theorems about injective metric spaces
• Λ-trees and their applications
• Modular Interval Spaces
• Relations related to betweenness: their structure and automorphisms

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