{
  "id": "2303.10194",
  "version": "v1",
  "published": "2023-03-17T18:07:17.000Z",
  "updated": "2023-03-17T18:07:17.000Z",
  "title": "$\\mathcal I^K$-limit points, $\\mathcal I^K$-cluster points and $\\mathcal I^K$-Frechet compactness",
  "authors": [
    "Manoranjan Singha",
    "Sima Roy"
  ],
  "comment": "14 pages, 1 figures",
  "categories": [
    "math.GN"
  ],
  "abstract": "In 2011, the theory of $\\mathcal I^K$-convergence gets birth as an extension of the concept of $\\mathcal{I}^*$-convergence of sequences of real numbers. $\\mathcal I^K$-limit points and $\\mathcal I^K$-cluster points of functions are introduced and studied to some extent, where $\\mathcal{I}$ and $\\mathcal{K}$ are ideals on a non-empty set $S$. In a first countable space set of $\\mathcal I^K$-cluster points is coincide with the closure of all sets in the filter base $\\mathcal{B}_f(\\mathcal{I^K})$ for some function $f : S\\to X$. Frechet compactness is studied in light of ideals $\\mathcal{I}$ and $\\mathcal{K}$ of subsets of $S$ and showed that in $\\mathcal{I}$-sequential $T_2$ space frechet compactness and $\\mathcal{I}$-frechet compactness are equivalent. A class of ideals have been identified for which $\\mathcal I^K$-frechet compactness coincides with $\\mathcal{I}$-frechet compactness in first countable spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-17T18:07:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D35",
      "54D45",
      "54D55"
    ],
    "keywords": [
      "cluster points",
      "limit points",
      "frechet compactness coincides",
      "first countable space set",
      "space frechet compactness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}