{
  "id": "1307.1989",
  "version": "v1",
  "published": "2013-07-08T09:10:09.000Z",
  "updated": "2013-07-08T09:10:09.000Z",
  "title": "Strong colorings yield kappa-bounded spaces with discretely untouchable points",
  "authors": [
    "Istvan Juhasz",
    "Saharon Shelah"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "It is well-known that every non-isolated point in a compact Hausdorff space is the accumulation point of a discrete subset. Answering a question raised by Z. Szentmiklossy and the first author, we show that this statement fails for countably compact regular spaces, and even for omega-bounded regular spaces. In fact, there are kappa-bounded counterexamples for every infinite cardinal kappa. The proof makes essential use of the so-called 'strong colorings' that were invented by the second author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-08T09:10:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A35",
      "03E35",
      "54A25"
    ],
    "keywords": [
      "strong colorings yield kappa-bounded spaces",
      "discretely untouchable points",
      "infinite cardinal kappa",
      "compact hausdorff space",
      "countably compact regular spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.1989J"
    }
  }
}