{
  "id": "2404.03848",
  "version": "v1",
  "published": "2024-04-05T00:46:14.000Z",
  "updated": "2024-04-05T00:46:14.000Z",
  "title": "On sncc-inheritance of pointwise almost periodicity in flows",
  "authors": [
    "Xiongping Dai"
  ],
  "comment": "17 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $H$ be a subnormal co-compact closed subgroup of a Hausdorff topological group $T$ and $X$ a compact Hausdorff space. We prove the inheritance theorem: A point of $X$ is almost periodic (a.p.) for $T\\curvearrowright X$ iff it is a.p. for $H\\curvearrowright X$. Moreover, if $T\\curvearrowright X$ is minimal with $H\\lhd T$, then $\\mathscr{O}_H\\colon X\\rightarrow2^X$, ${x\\mapsto\\overline{Hx}}$ is a continuous mapping, and, $T\\curvearrowright X/H$ is an a.p. nontrivial factor of $T\\curvearrowright X$ iff $T\\curvearrowright X\\times T/H$ is not minimal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-05T00:46:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05"
    ],
    "keywords": [
      "sncc-inheritance",
      "periodicity",
      "subnormal co-compact closed subgroup",
      "compact hausdorff space",
      "nontrivial factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}