{
  "id": "1502.06999",
  "version": "v1",
  "published": "2015-02-24T22:57:16.000Z",
  "updated": "2015-02-24T22:57:16.000Z",
  "title": "Isomorphic extensions and applications",
  "authors": [
    "Tomasz Downarowicz",
    "Eli Glasner"
  ],
  "comment": "16 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "If $\\pi:(X,T)\\to(Z,S)$ is a topological factor map between uniquely ergodic topological dynamical systems, then $(X,T)$ is called an isomorphic extension of $(Z,S)$ if $\\pi$ is also a measure-theoretic isomorphism. We consider the case when the systems are minimal and we pay special attention to equicontinuous $(Z,S)$. We first establish a characterization of this type of isomorphic extensions in terms of mean equicontinuity, and then show that an isomorphic extension need not be almost one-to-one, answering questions of Li, Tu and Ye.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-24T22:57:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "37B05"
    ],
    "keywords": [
      "isomorphic extension",
      "applications",
      "pay special attention",
      "topological factor map",
      "measure-theoretic isomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}