{
  "id": "2103.00102",
  "version": "v1",
  "published": "2021-02-27T01:57:01.000Z",
  "updated": "2021-02-27T01:57:01.000Z",
  "title": "A characterization of the product of the rational numbers and complete Erdős space",
  "authors": [
    "Rodrigo Hernández-Gutiérrez",
    "Alfredo Zaragoza"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "Erd\\H{o}s space $\\mathfrak{E}$ and complete Erd\\H{o}s space $\\mathfrak{E}_c$ have been previously shown to have topological characterizations. In this paper, we provide a topological characterization of the topological space $\\mathbb{Q}\\times\\mathfrak{E}_c$, where $\\mathbb{Q}$ is the space of rational numbers. As a corollary, we show that the Vietoris hyperspace of finite sets $\\mathcal{F}(\\mathfrak{E}_c)$ is homeomorphic to $\\mathbb{Q}\\times\\mathfrak{E}_c$. We also characterize the factors of $\\mathbb{Q}\\times\\mathfrak{E}_c$. An interesting open question that is left open is whether $\\sigma{\\mathfrak{E}_c}^\\omega$, the $\\sigma$-product of countably many copies of $\\mathfrak{E}_c$, is homeomorphic to $\\mathbb{Q}\\times\\mathfrak{E}_c$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-27T01:57:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F65",
      "54F50",
      "54A10",
      "54B20",
      "54H05"
    ],
    "keywords": [
      "complete erdős space",
      "rational numbers",
      "topological characterization",
      "vietoris hyperspace",
      "left open"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}