{
  "id": "1510.07291",
  "version": "v1",
  "published": "2015-10-25T19:15:21.000Z",
  "updated": "2015-10-25T19:15:21.000Z",
  "title": "On the Topology of Metric Spaces definable in o-minimal expansions of fields",
  "authors": [
    "Erik Walsberg"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We study the topology of metric spaces which are definable in o-minimal expansions of ordered fields. We show that a definable metric space either contains an infinite definable discrete set or is definably homeomorphic to a definable set equipped with its euclidean topology. This implies that a separable metric space which is definable in an o-minimal expansion of the real field is definably homeomorphic to a definable set equipped with its euclidean topology. We show that almost every point in a definable metric space has a neighborhood which is definably homeomorphic to an open definable subset of euclidean space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-25T19:15:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "o-minimal expansion",
      "metric spaces definable",
      "definable metric space",
      "definably homeomorphic",
      "euclidean topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151007291W"
    }
  }
}