{
  "id": "2210.08544",
  "version": "v1",
  "published": "2022-10-16T14:00:26.000Z",
  "updated": "2022-10-16T14:00:26.000Z",
  "title": "On $\\mathcal{I}$-covering images of metric spaces",
  "authors": [
    "Xiangeng Zhou",
    "Shou Lin"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "Let $\\mathcal{I}$ be an ideal on $\\mathbb{N}$. A mapping $f:X\\to Y$ is called an $\\mathcal{I}$-covering mapping provided a sequence $\\{y_{n}\\}_{n\\in\\mathbb N}$ is $\\mathcal{I}$-converging to a point $y$ in $Y$, there is a sequence $\\{x_{n}\\}_{n\\in\\mathbb N}$ converging to a point $x$ in $X$ such that $x\\in f^{-1}(y)$ and each $x_n\\in f^{-1}(y_n)$. In this paper we study the spaces with certain $\\mathcal{I}$-$cs$-networks and investigate the characterization of the images of metric spaces under certain $\\mathcal{I}$-covering mappings, which prompts us to discover $\\mathcal{I}$-$csf$-networks. The following main results are obtained: (1) A space $X$ has an $\\mathcal{I}$-$csf$-network if and only if $X$ is a continuous and $\\mathcal{I}$-covering image of a metric space. (2) A space $X$ is an $\\mathcal{I}$-$csf$-countable space if and only if $X$ is a continuous $\\mathcal{I}$-covering and boundary $s$-image of a metric space. (3) A space $X$ has a point-countable $\\mathcal{I}$-$cs$-network if and only if $X$ is a continuous $\\mathcal{I}$-covering and $s$-image of a metric space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-16T14:00:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A20",
      "54B15",
      "54C08",
      "54C10",
      "54D55",
      "54E20",
      "54E40",
      "54E99"
    ],
    "keywords": [
      "metric space",
      "covering image",
      "main results",
      "covering mapping",
      "continuous"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}