{
  "id": "1908.08521",
  "version": "v1",
  "published": "2019-08-22T17:52:48.000Z",
  "updated": "2019-08-22T17:52:48.000Z",
  "title": "On the dichotomy of a locally compact semitopological monoid of order isomorphisms between principal filters of $\\mathbb{N}^n$ with adjoined zero",
  "authors": [
    "Taras Mokrytskyi"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "Let $n$ be any positive integer and $\\mathscr{I\\!P\\!F}(\\mathbb{N}^n)$ be the semigroup of all order isomorphisms between principal filters of the $n$-th power of the set of positive integers $\\mathbb{N}$ with the product order. We prove that a Hausdorff locally compact semitopological semigroup ${\\mathscr{I\\!P\\!F}(\\mathbb{N}^n)}$ with an adjoined zero is either compact or discrete.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-22T17:52:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "locally compact semitopological monoid",
      "order isomorphisms",
      "principal filters",
      "adjoined zero",
      "hausdorff locally compact semitopological semigroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}