{
  "id": "1008.1175",
  "version": "v2",
  "published": "2010-08-06T12:50:21.000Z",
  "updated": "2010-09-22T08:57:40.000Z",
  "title": "Pontryagin duality between compact and discrete abelian inverse monoids",
  "authors": [
    "Taras Banakh",
    "Olena Hryniv"
  ],
  "comment": "8 pages",
  "categories": [
    "math.GN",
    "math.GR",
    "math.RA"
  ],
  "abstract": "For a topological monoid S the dual inverse monoid is the topological monoid of all identity preserving homomorphisms from S to the circle with attached zero. A topological monoid S is defined to be reflexive if the canonical homomorphism from S to its second dual inverse monoid is a topological isomorphism. We prove that a (compact or discrete) topological inverse monoid S is reflexive (if and) only if S is abelian and the idempotent semilattice of S is zero-dimensional. For a discrete (resp. compact) topological monoid its dual inverse monoid is compact (resp. discrete). These results unify the Pontryagin-van Kampen Duality Theorem for abelian groups and the Hofmann-Mislove-Stralka Duality Theorem for zero-dimensional topological semilattices.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-22T08:57:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D35"
    ],
    "keywords": [
      "discrete abelian inverse monoids",
      "pontryagin duality",
      "topological monoid",
      "second dual inverse monoid",
      "pontryagin-van kampen duality theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.1175B"
    }
  }
}