Metric spaces in which many triangles are degenerate
Metric Geometry
2023-10-30 v2
Abstract
Richmond and Richmond (Amer. Math. Monthly 104 (1997), 713--719) proved the following theorem: If, in a metric space with at least five points, all triangles are degenerate, then the space is isometric to a subset of the real line. We prove that the hypothesis is unnecessarily strong: In fact, suitably placed degenerate triangles suffice.
Cite
@article{arxiv.2209.14361,
title = {Metric spaces in which many triangles are degenerate},
author = {Vašek Chvátal and Ida Kantor},
journal= {arXiv preprint arXiv:2209.14361},
year = {2023}
}