{
  "id": "1906.10832",
  "version": "v1",
  "published": "2019-06-26T03:52:12.000Z",
  "updated": "2019-06-26T03:52:12.000Z",
  "title": "Existence of well-filterifications of $T_0$ topological spaces",
  "authors": [
    "Guohua Wu",
    "Xiaoyong Xi",
    "Xiaoquan Xu",
    "Dongsheng Zhao"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We prove that for every $T_0$ space $X$, there is a well-filtered space $W(X)$ and a continuous mapping $\\eta_X: X\\lra W(X)$ such that for any well-filtered space $Y$ and any continuous mapping $f: X\\lra Y$ there is a unique continuous mapping $\\hat{f}: W(X)\\lra Y$ such that $f=\\hat{f}\\circ \\eta_X$. Such a space $W(X)$ will be called the well-filterification of $X$. This result gives a positive answer to one of the major open problems on well-filtered spaces. Another result on well-filtered spaces we will prove is that the product of two well-filtered spaces is well-filtered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-26T03:52:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06B35",
      "06B30",
      "54A05"
    ],
    "keywords": [
      "well-filtered space",
      "topological spaces",
      "well-filterification",
      "continuous mapping"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}