{
  "id": "1903.01586",
  "version": "v1",
  "published": "2019-03-04T23:28:33.000Z",
  "updated": "2019-03-04T23:28:33.000Z",
  "title": "Proximity inductive dimension and Brouwer dimension agree on compact Hausdorff spaces",
  "authors": [
    "Jeremy Siegert"
  ],
  "comment": "8 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper we show that the proximity inductive dimension defined by Isbell agrees with the Brouwer dimension originally described by Brouwer on the class of compact Hausdorff spaces. Consequently, Fedorchuk's example of a compact Hausdorff space whose Brouwer dimension exceeds its Lebesgue covering dimension is an example of a space whose proximity inductive dimension exceeds its proximity dimension as defined by Smirnov.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-04T23:28:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact hausdorff space",
      "brouwer dimension agree",
      "brouwer dimension exceeds",
      "proximity inductive dimension exceeds",
      "lebesgue covering dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}