{
  "id": "1404.0151",
  "version": "v1",
  "published": "2014-04-01T07:55:53.000Z",
  "updated": "2014-04-01T07:55:53.000Z",
  "title": "Topological infinite gammoids, and a new Menger-type theorem for infinite graphs",
  "authors": [
    "Johannes Carmesin"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Answering a question of Diestel, we develop a topological notion of gammoids in infinite graphs which, unlike traditional infinite gammoids, always define a matroid. As our main tool, we prove for any infinite graph $G$ with vertex sets $A$ and $B$ that if every finite subset of $A$ is linked to $B$ by disjoint paths, then the whole of $A$ can be linked to the closure of $B$ by disjoint paths or rays in a natural topology on $G$ and its ends. This latter theorem re-proves and strengthens the infinite Menger theorem of Aharoni and Berger for `well-separated' sets $A$ and $B$. It also implies the topological Menger theorem of Diestel for locally finite graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-01T07:55:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C63"
    ],
    "keywords": [
      "infinite graph",
      "topological infinite gammoids",
      "menger-type theorem",
      "disjoint paths",
      "infinite menger theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.0151C"
    }
  }
}