{
  "id": "1607.03826",
  "version": "v1",
  "published": "2016-07-13T17:02:25.000Z",
  "updated": "2016-07-13T17:02:25.000Z",
  "title": "Absoluteness of $F_{σδ}$ property",
  "authors": [
    "Vojtěch Kovařík"
  ],
  "comment": "This is an early version of the paper, which is to be presented at Toposym 2016 conference",
  "categories": [
    "math.GN"
  ],
  "abstract": "In general topology, the class of \\v{C}ech-complete spaces is well studied. A space $X$ is \\v{C}ech-complete, if it is a $G_\\delta$ subset of its \\v{C}ech-Stone compactification $\\beta X$, and this is equivalent to $X$ being a $G_\\delta$ subset of its every compactification. In functional analysis, one naturally encounters many spaces which, when equipped with weak topology, are $F_{\\sigma\\delta}$ rather than $G_\\delta$ subsets of some of their compactifications. For example, all separable Banach spaces (or more generally, all WCG Banach spaces) enjoy this property. However, this property is not \"absolute\" - a Banach space can be $F_{\\sigma\\delta}$ in some, but not all of its compactifications.\\vknote{Possibly add a reference here} We study topological spaces which are $F_{\\sigma\\delta}$ in some of their compactifications, giving for each such $X$ a wider class of compactifications which all contain $X$ as an $F_{\\sigma\\delta}$ subset.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-13T17:02:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H05"
    ],
    "keywords": [
      "compactification",
      "absoluteness",
      "wcg banach spaces",
      "general topology",
      "wider class"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}