{
  "id": "1410.6778",
  "version": "v1",
  "published": "2014-10-24T18:53:43.000Z",
  "updated": "2014-10-24T18:53:43.000Z",
  "title": "Divisibility in the Stone-Čech compactification",
  "authors": [
    "Boris Šobot"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Cech compactification \\beta N, we establish some results about one of such extensions. This provides us with one possible divisibility relation on \\beta N and we introduce a few more, defined in a natural way. For some of them we find equivalent conditions for divisibility. Finally, we mention a few facts about prime and irreducible elements of (\\beta N, \\cdot). The motivation behind all this is to try to translate problems in number theory into \\beta N.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-24T18:53:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D35",
      "54D80",
      "22A15"
    ],
    "keywords": [
      "stone-čech compactification",
      "number theory",
      "extensions",
      "translate problems",
      "binary relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.6778S"
    }
  }
}