A New Proof for the Characterization of Linear Betweenness Structure

2017/07/03 by Péter G. N. Szabó, Szabó, Péter G. N.
Mathematics · Engineering · #Fixed Point Theorems Analysis #Mathematics and Applications #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.1707.00659

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.

Related

• Betweenness Structures of Small Linear Co-Size
• Metric spaces in which many triangles are degenerate
• Metric Spaces in Which Many Triangles Are Degenerate
• Quasimetric spaces with few lines
• Ultrametricity and metric betweenness in tangent spaces to metric spaces