{
  "id": "1409.6324",
  "version": "v1",
  "published": "2014-09-22T20:02:23.000Z",
  "updated": "2014-09-22T20:02:23.000Z",
  "title": "A complete classification of homogeneous plane continua",
  "authors": [
    "L. C. Hoehn",
    "L. G. Oversteegen"
  ],
  "comment": "26 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "We show that every non-degenerate homogeneous plane continuum is homeomorphic to either the unit circle, the pseudo-arc, or the circle of pseudo-arcs. It follows that any planar homogenous compactum has the form $X \\times Z$, where $X$ is a either a point or one of these three homogeneous plane continua, and $Z$ is a finite set or the Cantor set. The main technical result in this paper is a new characterization of the pseudo-arc: a non-degenerate continuum is homeomorphic to the pseudo-arc if and only if it is hereditarily indecomposable and has span zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-22T20:02:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F15",
      "54F65"
    ],
    "keywords": [
      "complete classification",
      "pseudo-arc",
      "non-degenerate homogeneous plane continuum",
      "unit circle",
      "planar homogenous compactum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.6324H"
    }
  }
}