{
  "id": "2103.14841",
  "version": "v1",
  "published": "2021-03-27T08:31:23.000Z",
  "updated": "2021-03-27T08:31:23.000Z",
  "title": "On $I^K$-Convergence in a Topological space via semi-open sets",
  "authors": [
    "Ankur Sharmah",
    "Debajit Hazarika"
  ],
  "comment": "8 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "In this article, we consider $\\mathcal{I}^\\mathcal{K}$-convergence to define a new concept of convergence namely, $\\mathcal{S}$-$\\mathcal{I}^\\mathcal{K}$-convergence which generalizes the notion of $\\mathcal{S}$-$\\mathcal{I}$-convergence introduced by Guevara et al. \\cite{GSR20} recently. Some properties of $\\mathcal{S}$-$\\mathcal{I}^\\mathcal{K}$-convergence of sequences and its relation with compact sets are discussed. In particular, we investigate the relation between semi-compactness and semi-Lindeloffness by introducing the notion of $\\mathcal{S}$-$\\mathcal{I}^\\mathcal{K}$-cluster point of a sequence. The \"Equivalence between semi-dense and dense sets\" is utilized to characterize the set of $\\mathcal{S}$-$\\mathcal{I}^\\mathcal{K}$-cluster points of a sequence as semi-closed subsets of a topological space. Moreover, in product space, we obtain some results for $\\mathcal{I}^\\mathcal{K}$-convergence which also holds for $\\mathcal{S}$-$\\mathcal{I}^\\mathcal{K}$-convergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-27T08:31:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A20",
      "40A05",
      "40A35"
    ],
    "keywords": [
      "convergence",
      "topological space",
      "semi-open sets",
      "cluster point",
      "compact sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}