{
  "id": "2002.07010",
  "version": "v1",
  "published": "2020-02-17T15:44:30.000Z",
  "updated": "2020-02-17T15:44:30.000Z",
  "title": "On cohesive almost zero-dimensional spaces",
  "authors": [
    "Jan J. Dijkstra",
    "David S. Lipham"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "We investigate C-sets in almost zero-dimensional spaces, showing that closed $\\sigma$C-sets are C-sets. As corollaries, we prove that every rim-$\\sigma$-compact almost zero-dimensional space is zero-dimensional and that each cohesive almost zero-dimensional space is nowhere rational. To show these results are sharp, we construct a rim-discrete connected set with an explosion point. We also show every cohesive almost zero-dimensional subspace of $($Cantor set$)$$\\times\\mathbb R$ is nowhere dense.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-17T15:44:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F45",
      "54F50",
      "54D35",
      "54G20"
    ],
    "keywords": [
      "zero-dimensional space",
      "rim-discrete connected set",
      "explosion point",
      "zero-dimensional subspace",
      "cantor set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}