{
  "id": "1510.07196",
  "version": "v1",
  "published": "2015-10-25T01:11:29.000Z",
  "updated": "2015-10-25T01:11:29.000Z",
  "title": "The Hausdorff dimension of metric spaces definable in o-minimal expansions of the real field",
  "authors": [
    "Jana Maříková",
    "Erik Walsberg"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let $R$ be an o-minimal expansion of the real field. We show that the Hausdorff dimension of an $R$-definable metric space is an $R$-definable function of the parameters defining the metric space. We also show that the Hausdorff dimension of an $R$-definable metric space is an element of the field of powers of $R$. The proof uses a basic topological dichotomy for definable metric spaces due to the second author, and the work of the first author and Shiota on measure theory over nonarchimedean o-minimal structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-25T01:11:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hausdorff dimension",
      "metric spaces definable",
      "o-minimal expansion",
      "real field",
      "definable metric space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151007196M"
    }
  }
}