{
  "id": "2305.03166",
  "version": "v1",
  "published": "2023-05-04T21:42:25.000Z",
  "updated": "2023-05-04T21:42:25.000Z",
  "title": "C-open Sets on Topological Spaces",
  "authors": [
    "M. H. Alqahtani"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "An open (resp., closed) subset A of a topological space (X, T ) is called C-open (resp., C-closed) set if cl(A) \\ A (resp., A \\ int(A)) is a countable set. This paper aims to present the concept of C-open and C-closed sets. We first investigate their basic properties. Then, we found some operators such as interior, closure, limit, border, and frontier using C-open and C-closed sets. The relationships between them are clarified and discussed. Finally, we exhibit continuous maps and compact space defined using C-open and C-closed sets and scrutinize their main properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-04T21:42:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A05",
      "54C10",
      "54D30"
    ],
    "keywords": [
      "topological space",
      "c-open sets",
      "c-closed sets",
      "basic properties",
      "compact space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}