{
  "id": "1603.07459",
  "version": "v1",
  "published": "2016-03-24T07:49:05.000Z",
  "updated": "2016-03-24T07:49:05.000Z",
  "title": "Completeness and compactness properties in metric spaces, topological groups and function spaces",
  "authors": [
    "Alejandro Dorantes-Aldama",
    "Dmitri Shakhmatov"
  ],
  "categories": [
    "math.GN",
    "math.FA",
    "math.GR"
  ],
  "abstract": "We prove that many completeness properties coincide in metric spaces, precompact groups and dense subgroups of products of separable metric groups. We apply these results to function spaces C_p(X,G) of G-valued continuous functions on a space X with the topology of pointwise convergence, for a separable metric group G. Not only the results but also the proofs themselves are novel even in the classical case when G is the real line. A space X is weakly pseudocompact if it is G_delta-dense in at least one of its compactifications. A topological group G is precompact if it is topologically isomorphic to a subgroup of a compact group. We prove that every weakly pseudocompact precompact topological group is pseudocompact, thereby answering positively a question of Tkachenko.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-24T07:49:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A05",
      "46E10",
      "54C30",
      "54D70",
      "54E50",
      "54E52"
    ],
    "keywords": [
      "function spaces",
      "metric spaces",
      "compactness properties",
      "separable metric group",
      "weakly pseudocompact precompact topological group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160307459D"
    }
  }
}