{
  "id": "1802.08341",
  "version": "v1",
  "published": "2018-02-22T23:09:28.000Z",
  "updated": "2018-02-22T23:09:28.000Z",
  "title": "Embeddability on functions: order and chaos",
  "authors": [
    "Raphaël Carroy",
    "Yann Pequignot",
    "Zoltán Vidnyánszky"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We study the quasi-order of topological embeddability on definable functions between Polish zero-dimensional spaces. We first study the descriptive complexity of this quasi-order restricted to the space of continuous functions. Our main result is the following dichotomy: the embeddability quasi-order restricted to continuous functions from a given compact space to another is either an analytic complete quasi-order or a well-quasi-order. We then turn to the existence of maximal elements with respect to embeddability in a given Baire class. It is proved that the class of continuous functions is the only Baire class to admit a maximal element. We prove that no Baire class admits a maximal element, except for the class of continuous functions which admits a maximum element.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-22T23:09:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "26A21",
      "54C05",
      "54C25",
      "06A07"
    ],
    "keywords": [
      "embeddability",
      "continuous functions",
      "maximal element",
      "baire class admits",
      "analytic complete quasi-order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}