{
  "id": "2408.07548",
  "version": "v1",
  "published": "2024-08-14T13:37:28.000Z",
  "updated": "2024-08-14T13:37:28.000Z",
  "title": "On the probabilistic metrizability of approach spaces",
  "authors": [
    "Hongliang Lai",
    "Lili Shen",
    "Junche Yu"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GN",
    "math.CT"
  ],
  "abstract": "We investigate approach spaces generated by probabilistic metric spaces with respect to a continuous t-norm $*$ on the unit interval $[0,1]$. Let $k^*$ be the supremum of the idempotent elements of $*$ in $[0,1)$. It is shown that if $k^*=1$ (resp. $k^*<1$), then an approach space is probabilistic metrizable with respect to $*$ if and only if it is probabilistic metrizable with respect to the minimum (resp. product) t-norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-14T13:37:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A05",
      "54E70",
      "54E35"
    ],
    "keywords": [
      "approach space",
      "probabilistic metrizability",
      "probabilistic metric spaces",
      "unit interval",
      "probabilistic metrizable"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}