{
  "id": "1904.12203",
  "version": "v1",
  "published": "2019-04-27T20:22:03.000Z",
  "updated": "2019-04-27T20:22:03.000Z",
  "title": "On equicontinuous factors of flows on locally path-connected compact spaces",
  "authors": [
    "Nikolai Edeko"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider a locally path-connected compact metric space $K$ with finite first Betti number $b_1(K)$ and a flow $(K, G)$ on $K$ such that $G$ is abelian and all $G$-invariant functions $f\\in\\mathrm{C}(K)$ are constant. We prove that every equicontinuous factor of the flow $(K, G)$ is isomorphic to a flow on a compact abelian Lie group of dimension less than $b_1(K)$. For this purpose, we use and provide a new proof for [HJop, Theorem 2.12] which states that for a flow on a locally connected compact space the quotient map onto the maximal equicontinuous factor is monotone, i.e., has connected fibers. Our alternative proof is a simple consequence of a new characterization of the monotonicity of a quotient map $p\\colon K\\to L$ between locally connected compact spaces $K$ and $L$ that we obtain by characterizing the local connectedness of $K$ in terms of the Banach lattice $\\mathrm{C}(K)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-27T20:22:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H20",
      "37B05"
    ],
    "keywords": [
      "locally path-connected compact spaces",
      "equicontinuous factor",
      "path-connected compact metric space",
      "locally connected compact space",
      "quotient map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}