{
  "id": "2410.12503",
  "version": "v1",
  "published": "2024-10-16T12:27:43.000Z",
  "updated": "2024-10-16T12:27:43.000Z",
  "title": "On sparse set topology using ideals in the space of reals",
  "authors": [
    "Indrajit Debnath",
    "Amar Kumar Banerjee"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper we have introduced the notion of $\\mathcal{I}$-sparse set in the space of reals and explored some properties of the family of $\\mathcal{I}$-sparse sets. Thereafter we have induced a topology namely $\\mathcal{I}$-sparse set topology in the space of reals and it has been observed that this topology is finer than $\\mathcal{I}-$density topology introduced by Banerjee and Debnath in \\cite{banerjee 4}. We further studied some salient properties of this topology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-16T12:27:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26E99",
      "54C30",
      "40A35"
    ],
    "keywords": [
      "sparse set topology",
      "salient properties",
      "density topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}