{
  "id": "1207.7004",
  "version": "v1",
  "published": "2012-07-30T17:30:47.000Z",
  "updated": "2012-07-30T17:30:47.000Z",
  "title": "Injections into Function Spaces over Compacta",
  "authors": [
    "Raushan Z. Buzyakova"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "We study the topology of X given that Cp(X) injects into Cp(Y), where Y is compact. We first show that if Cp over a GO-space (=\"subspace of a lineraly ordered space\") injects into Cp over a compactum, then the Dedekind remainder of the GO-space is hereditarily paracompact. Also, for each ordinal tau of uncountable cofinality, we construct a continuous bijection of Cp(tau, {0,1}) onto a subgroup of Cp(tau+1, {0,1}), which is in addition a group isomorphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-30T17:30:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C35",
      "54C10"
    ],
    "keywords": [
      "function spaces",
      "injections",
      "dedekind remainder",
      "ordinal tau",
      "group isomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.7004B"
    }
  }
}