{
  "id": "2406.15772",
  "version": "v1",
  "published": "2024-06-22T07:45:42.000Z",
  "updated": "2024-06-22T07:45:42.000Z",
  "title": "Center and radius of a subset of metric space",
  "authors": [
    "Akhilesh Badra",
    "Hemant Kumar Singh"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper, we introduce a notion of the center and radius of a subset A of metric space X. In the Euclidean spaces, this notion can be seen as the extension of the center and radius of open/closed balls. The center and radius of a finite product of subsets of metric spaces, and a finite union of subsets of a metric space are also determined. For any subset A of metric space X, there is a natural question to identify the open balls of X with the largest radius that are entirely contained in A. To answer this question, we introduce a notion of quasi-center and quasi-radius of a subset A of metric space X. We prove that the center of the largest open balls contained in A belongs to the quasi-center of A, and its radius is equal to the quasi-radius of A. In particular, for the Euclidean spaces, we see that the center of largest open balls contained in A belongs to the center of A, and its radius is equal to the radius of A.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-22T07:45:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54E35",
      "54E99"
    ],
    "keywords": [
      "metric space",
      "largest open balls",
      "euclidean spaces",
      "finite product",
      "quasi-radius"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}