{
  "id": "1806.09015",
  "version": "v1",
  "published": "2018-06-23T18:03:32.000Z",
  "updated": "2018-06-23T18:03:32.000Z",
  "title": "Classification of spaces of Continuous Function on ordinals",
  "authors": [
    "L. V. Genze",
    "S. P. Gul'ko",
    "T. E. Khmyleva"
  ],
  "comment": "7 pages; accepted by Commentationes Mathematicae Universitatis Carolinae",
  "categories": [
    "math.GN",
    "math.FA"
  ],
  "abstract": "We conclude the classification of spaces of continuous functions on ordinals carried out by R. Gorak. This gives a complete topological classification of the spaces $C_p([0,\\alpha])$ of all continuous real-valued functions on compact segments of ordinals endowed with the topology of pointwise convergence. Moreover, this topological classification of the spaces $C_p([0,\\alpha])$ completely coincides with their uniform classification.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-23T18:03:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous function",
      "uniform classification",
      "compact segments",
      "complete topological classification",
      "pointwise convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}