{
  "id": "2410.13150",
  "version": "v1",
  "published": "2024-10-17T02:08:46.000Z",
  "updated": "2024-10-17T02:08:46.000Z",
  "title": "A well-quasi-order for continuous functions",
  "authors": [
    "Raphaël Carroy",
    "Yann Pequignot"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove that continuous reducibility is a well-quasi-order on the class of continuous functions between separable metrizable spaces with analytic zero-dimensional domain. To achieve this, we define scattered functions, which generalize scattered spaces, and describe exhaustively scattered functions between zero-dimensional separable metrizable spaces up to continuous equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-17T02:08:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "26A21",
      "54C05",
      "03D55",
      "06A07"
    ],
    "keywords": [
      "continuous functions",
      "well-quasi-order",
      "analytic zero-dimensional domain",
      "define scattered functions",
      "zero-dimensional separable metrizable spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}