{
  "id": "math/0507062",
  "version": "v1",
  "published": "2005-07-04T12:41:16.000Z",
  "updated": "2005-07-04T12:41:16.000Z",
  "title": "Small Valdivia compact spaces",
  "authors": [
    "Wieslaw Kubiś",
    "Henryk Michalewski"
  ],
  "comment": "20 pages",
  "journal": "Topology Appl. 153 (2006), no. 14, 2560--2573",
  "doi": "10.1016/j.topol.2005.09.010",
  "categories": [
    "math.GN",
    "math.FA"
  ],
  "abstract": "We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of ``simple'' retractions. Consequently, a compact space of weight $\\loe\\aleph_1$ is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight at most $\\aleph_1$ is preserved both under retractions and under open 0-dimensional images. Finally, we characterize the class of all Valdivia compacta in the language of category theory, which implies that this class is preserved under all continuous weight preserving functors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-04T12:41:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D30",
      "54C15",
      "54B35"
    ],
    "keywords": [
      "small valdivia compact spaces",
      "valdivia compacta",
      "inverse sequence",
      "retractions",
      "continuous weight preserving functors"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7062K"
    }
  }
}