{
  "id": "1805.01560",
  "version": "v1",
  "published": "2018-05-03T22:27:00.000Z",
  "updated": "2018-05-03T22:27:00.000Z",
  "title": "Separation axioms and covering dimension of asymmetric normed spaces",
  "authors": [
    "Victor Donjuán",
    "Natalia Jonard-Pérez"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper, we approach the question if some of the separation axioms are equivalent in the class of asymmetric normed spaces. In particular, we make a remark on a known theorem which states that every $T_1$ asymmetric normed space with compact closed unit ball must be finite-dimensional. We also explore the product structure of these spaces and characterize the topological (covering) dimension of all finite-dimensional asymmetric normed spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-03T22:27:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A30",
      "46A19",
      "52A21",
      "54D10",
      "54F45",
      "54H11"
    ],
    "keywords": [
      "separation axioms",
      "covering dimension",
      "compact closed unit ball",
      "finite-dimensional asymmetric normed spaces",
      "product structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}