{
  "id": "math/0010261",
  "version": "v2",
  "published": "2000-10-27T12:03:07.000Z",
  "updated": "2001-05-14T14:19:06.000Z",
  "title": "Realcompactness and spaces of vector-valued functions",
  "authors": [
    "Jesus Araujo"
  ],
  "comment": "15 pages, LaTeX. Results stated for arbitrary normed spaces without changes in proofs. New presentation and new examples. One reference added",
  "categories": [
    "math.GN",
    "math.FA"
  ],
  "abstract": "It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y; in particular we find remarkable differences with respect to the scalar context: namely, if E and F are infinite-dimensional and T is a biseparating map between the space of E-valued bounded continuous functions on X and that of F-valued bounded continuous functions on Y, then the realcompactifications of X and Y are homeomorphic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-05-14T14:19:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C35",
      "54C40",
      "54D60",
      "46E40"
    ],
    "keywords": [
      "vector-valued functions",
      "realcompactness",
      "biseparating map",
      "large class",
      "homeomorphic"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....10261A"
    }
  }
}