{
  "id": "2210.12099",
  "version": "v1",
  "published": "2022-10-21T16:52:12.000Z",
  "updated": "2022-10-21T16:52:12.000Z",
  "title": "Cop and robber on finite spaces",
  "authors": [
    "Jonathan A. Barmak"
  ],
  "comment": "21 pages, 18 figures",
  "categories": [
    "math.GN",
    "math.AT",
    "math.CO"
  ],
  "abstract": "A cop tries to capture a robber in a topological space $X$ being unable to see him. For which spaces $X$ does the cop have a strategy which allows him to capture the robber independently of his efforts to escape? In other words, when is there a curve $\\gamma: \\mathbb{R}_{\\ge 0}\\to X$ which has a coincidence with any other curve in $X$. We analyze in particular the case of finite topological spaces and discover general results and exotic examples about paths in these spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-21T16:52:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F65",
      "91A24",
      "91A44"
    ],
    "keywords": [
      "finite spaces",
      "cop tries",
      "finite topological spaces",
      "general results",
      "exotic examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}