{
  "id": "1106.3808",
  "version": "v1",
  "published": "2011-06-20T05:25:12.000Z",
  "updated": "2011-06-20T05:25:12.000Z",
  "title": "Regular Bases At Non-isolated Points And Metrization Theorems",
  "authors": [
    "Fucai Lin",
    "Shou Lin",
    "Heikki Junnila"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper, we define the spaces with a regular base at non-isolated points and discuss some metrization theorems. We firstly show that a space $X$ is a metrizable space, if and only if $X$ is a regular space with a $\\sigma$-locally finite base at non-isolated points, if and only if $X$ is a perfect space with a regular base at non-isolated points, if and only if $X$ is a $\\beta$-space with a regular base at non-isolated points. In addition, we also discuss the relations between the spaces with a regular base at non-isolated points and some generalized metrizable spaces. Finally, we give an affirmative answer for a question posed by F. C. Lin and S. Lin in \\cite{LL}, which also shows that a space with a regular base at non-isolated points has a point-countable base.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-20T05:25:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D70",
      "54E35",
      "54D20"
    ],
    "keywords": [
      "non-isolated points",
      "regular base",
      "metrization theorems",
      "regular space",
      "locally finite base"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.3808L"
    }
  }
}