A New Proof for the Characterization of Linear Betweenness Structure
Combinatorics
2020-06-02 v3
Abstract
In their paper published in 1997, Richmond and Richmond classified metric spaces in which all triangles are degenerate. That result was later reproved by Dovgoshei and Dordovskii in the finite case and it was generalized to finite pseudometric betweennesses by Beaudou et al. In this paper, we give a new, independent proof to the finite case of the original theorem which we reformulate in terms of linearity of betweenness structures.
Keywords
Cite
@article{arxiv.1707.00659,
title = {A New Proof for the Characterization of Linear Betweenness Structure},
author = {Péter G. N. Szabó},
journal= {arXiv preprint arXiv:1707.00659},
year = {2020}
}
Comments
10 pages, 3 figures Keywords: Finite metric space, Metric betweenness, Linearity, Degenerate triangles triangles