{
  "id": "0809.4733",
  "version": "v1",
  "published": "2008-09-27T02:56:24.000Z",
  "updated": "2008-09-27T02:56:24.000Z",
  "title": "Spaces with a Finite Family of Basic Functions",
  "authors": [
    "Paul Gartside",
    "Feng Ziqin"
  ],
  "doi": "10.1112/blms/bdq077",
  "categories": [
    "math.FA",
    "math.GN"
  ],
  "abstract": "A space X is finite dimensional, locally compact and separable metrizable if and only if X has a finite basic family: continuous functions Phi_1,...,Phi_n of X to the reals, R, such that for all continuous f from X to R there are g_1,..., g_n in C(R) satisfying f(x)=g_1(Phi_1(x))+g_2(Phi_2(x))+...+g_n(Phi_n(x)) for all x in X. This give the complete solution to four problems on basic functions posed by Sternfeld, as well as questions posed by Hattori and others.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-27T02:56:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B40",
      "54C30",
      "54C35",
      "54E45"
    ],
    "keywords": [
      "finite family",
      "finite dimensional",
      "complete solution",
      "finite basic family",
      "continuous functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4733G"
    }
  }
}