{
  "id": "2310.20690",
  "version": "v1",
  "published": "2023-10-31T17:53:52.000Z",
  "updated": "2023-10-31T17:53:52.000Z",
  "title": "A direct proof for the positive definiteness of four point metric spaces",
  "authors": [
    "Kiyonori Gomi"
  ],
  "comment": "LaTex 2e, 8 pages",
  "categories": [
    "math.MG"
  ],
  "abstract": "We provide a direct and elementary proof for the fact that every four point metric spaces are positive definite, which was first proved by Meckes based on some embedding theorems of metric spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-31T17:53:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51F99"
    ],
    "keywords": [
      "point metric spaces",
      "direct proof",
      "positive definiteness",
      "elementary proof",
      "embedding theorems"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}