{
  "id": "1911.07406",
  "version": "v1",
  "published": "2019-10-10T17:39:05.000Z",
  "updated": "2019-10-10T17:39:05.000Z",
  "title": "Dynamics Near An Idempotent",
  "authors": [
    "Md Moid Shaikh",
    "Sourav Kanti Patra"
  ],
  "comment": "15 pages, Comments and suggestions are welcome. arXiv admin note: substantial text overlap with arXiv:1711.06054",
  "categories": [
    "math.DS",
    "math.CO"
  ],
  "abstract": "Hindman and Leader first introduced the notion of semigroup of ultrafilters converging to zero for a dense subsemigroups of $((0,\\infty),+)$. Using the algebraic structure of the Stone-$\\breve{C}$ech compactification, Tootkabani and Vahed generalized and extended this notion to an idempotent instead of zero, that is a semigroup of ultrafilters converging to an idempotent $e$ for a dense subsemigroups of a semitopological semigroup $(T, +)$ and they gave the combinatorial proof of central set theorem near $e$. Algebraically one can also define quasi-central sets near $e$ for dense subsemigroups of $(T, +)$. In a dense subsemigroup of $(T,+)$, C-sets near $e$ are the sets, which satisfy the conclusions of the central sets theorem near $e$. S. K. Patra gave dynamical characterizations of these combinatorially rich sets near zero. In this paper we shall prove these dynamical characterizations for these combinatorially rich sets near $e$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-10T17:39:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B20",
      "37B05",
      "05B10"
    ],
    "keywords": [
      "dense subsemigroup",
      "idempotent",
      "combinatorially rich sets",
      "patra gave dynamical characterizations",
      "central set theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}