{
  "id": "1209.5451",
  "version": "v1",
  "published": "2012-09-24T23:09:45.000Z",
  "updated": "2012-09-24T23:09:45.000Z",
  "title": "n-Arc Connected Spaces",
  "authors": [
    "Benjamin Espinoza",
    "Paul Gartside",
    "Ana Mamatelashvili"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "A space is `n-arc connected' (n-ac) if any family of no more than n-points are contained in an arc. For graphs the following are equivalent: (i) 7-ac, (ii) n-ac for all n, (iii) continuous injective image of a closed sub-interval of the real line, and (iv) one of a finite family of graphs. General continua that are aleph_0-ac are characterized. The complexity of characterizing n-ac graphs for n=2,3,4,5 is determined to be strictly higher than that of the stated characterization of 7-ac graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-24T23:09:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F15"
    ],
    "keywords": [
      "n-arc connected spaces",
      "real line",
      "general continua",
      "characterizing n-ac graphs",
      "injective image"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.5451E"
    }
  }
}