{
  "id": "1504.08191",
  "version": "v1",
  "published": "2015-04-30T12:27:23.000Z",
  "updated": "2015-04-30T12:27:23.000Z",
  "title": "When all closed subsets are recurrent?",
  "authors": [
    "Jie Li",
    "Piotr Oprocha",
    "Xiangdong Ye",
    "Ruifeng Zhang"
  ],
  "comment": "30 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In the paper we study relations of rigidity, equicontinuity and pointwise recurrence between a t.d.s. $(X,T)$ and the t.d.s. $(K(X),T_K)$ induced on the hyperspace $K(X)$ of all compact subsets of $X$, and provide some characterizations. Among other examples, we construct a minimal, non-equicontinuous, distal and uniformly rigid t.d.s. and a t.d.s. which has dense small periodic sets but does not have dense distal points, solving that way open questions existing in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-30T12:27:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B20",
      "54H20",
      "37B20",
      "37B40"
    ],
    "keywords": [
      "closed subsets",
      "dense small periodic sets",
      "dense distal points",
      "way open questions existing",
      "compact subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150408191L"
    }
  }
}