{
  "id": "2208.06886",
  "version": "v1",
  "published": "2022-08-14T17:16:58.000Z",
  "updated": "2022-08-14T17:16:58.000Z",
  "title": "Hereditarily indecomposable continua as generic objects",
  "authors": [
    "Adam Bartoš",
    "Wiesław Kubiś"
  ],
  "comment": "63 pages, 2 figures, comments are welcome",
  "categories": [
    "math.GN",
    "math.CT",
    "math.LO"
  ],
  "abstract": "We develop an abstract approximate Fra\\\"iss\\'e theory in order to realize the pseudo-arc as well as P-adic pseudo-solenoids for sets of primes P as Fra\\\"iss\\'e limits. Our framework generalizes the discrete theory (classical and projective), but is also suitable for working directly with continuous maps on metrizable compacta. Moreover, we consider the abstract Banach--Mazur game played in a category and realize the pseudo-arc as well as all pseudo-solenoids (not necessarily P-adic) as generic objects.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-14T17:16:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F15",
      "18D20",
      "18F60"
    ],
    "keywords": [
      "generic objects",
      "hereditarily indecomposable continua",
      "abstract banach-mazur game",
      "abstract approximate",
      "pseudo-arc"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}