{
  "id": "1101.4504",
  "version": "v1",
  "published": "2011-01-24T11:34:25.000Z",
  "updated": "2011-01-24T11:34:25.000Z",
  "title": "Pontryagin duality in the class of precompact Abelian groups and the Baire property",
  "authors": [
    "Montserrat Bruguera",
    "Mikhail Tkachenko"
  ],
  "categories": [
    "math.GN",
    "math.GR"
  ],
  "abstract": "We present a wide class of reflexive, precompact, non-compact, Abelian topological groups $G$ determined by three requirements. They must have the Baire property, satisfy the \\textit{open refinement condition}, and contain no infinite compact subsets. This combination of properties guarantees that all compact subsets of the dual group $G^\\wedge$ are finite. We also show that many (non-reflexive) precompact Abelian groups are quotients of reflexive precompact Abelian groups. This includes all precompact almost metrizable groups with the Baire property and their products. Finally, given a compact Abelian group $G$ of weight $\\geq 2^\\om$, we find proper dense subgroups $H_1$ and $H_2$ of $G$ such that $H_1$ is reflexive and pseudocompact, while $H_2$ is non-reflexive and almost metrizable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-24T11:34:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A40",
      "22D35",
      "22C05",
      "54E52",
      "54C10"
    ],
    "keywords": [
      "baire property",
      "pontryagin duality",
      "reflexive precompact abelian groups",
      "proper dense subgroups",
      "infinite compact subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.4504B"
    }
  }
}