A direct proof for the positive definiteness of four point metric spaces
Metric Geometry
2023-12-05 v2
Abstract
We provide a direct and elementary proof for the fact that every four point metric space is positive definite, which was first proved by Meckes based on some embedding theorems of metric spaces. As an outcome of the direct proof, we also provide a condition for the magnitude of a finite metric space to obey the inclusion-exclusion principle with respect to a specific choice of subspaces.
Keywords
Cite
@article{arxiv.2310.20690,
title = {A direct proof for the positive definiteness of four point metric spaces},
author = {Kiyonori Gomi},
journal= {arXiv preprint arXiv:2310.20690},
year = {2023}
}
Comments
LaTex 2e, 17 pages; a section about the inclusion-exclusion principle added