{
  "id": "2102.12207",
  "version": "v1",
  "published": "2021-02-24T11:06:53.000Z",
  "updated": "2021-02-24T11:06:53.000Z",
  "title": "The weak compactification of locally compact groups",
  "authors": [
    "María V. Ferrer",
    "Salvador Hernández"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1704.03438",
  "categories": [
    "math.GN",
    "math.FA"
  ],
  "abstract": "We further investigate the weak topology generated by the irreducible unitary representations of a group $G$. A deep result due to Ernest \\cite{Ernest1971} and Hughes \\cite{Hughes1973} asserts that every weakly compact subset of a locally compact (LC) group $G$ is compact in the LC-topology, generalizing thereby a previous result of Glicksberg \\cite{glicks1962} for abelian locally compact (LCA) groups. Here, we first survey some recent findings on the weak topology and establish some new results about the preservation of several compact-like properties when going from the weak topology to the original topology of LC groups. Among others, we deal with the preservation of countably compactness, pseudocompactness and functional boundedness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-24T11:06:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "locally compact groups",
      "weak compactification",
      "weak topology",
      "irreducible unitary representations",
      "weakly compact subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}