{
  "id": "1804.09103",
  "version": "v1",
  "published": "2018-04-24T15:41:30.000Z",
  "updated": "2018-04-24T15:41:30.000Z",
  "title": "On the reflection of the countable chain condition",
  "authors": [
    "Ramiro de la Vega"
  ],
  "comment": "7 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "We study the question of when an uncountable ccc topological space $X$ contains a ccc subspace of size $\\aleph_1$. We show that it does if $X$ is compact Hausdorff and more generally if $X$ is Hausdorff with $\\mathrm{pct}(X) \\leq \\aleph_1$. For each regular cardinal $\\kappa$, an example is constructed of a ccc Tychonoff space of size $\\kappa$ and countable pseudocharacter but with no ccc subspace of size less than $\\kappa$. We also give a ccc compact $T_1$ space of size $\\kappa$ with no ccc subspace of size less than $\\kappa$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-24T15:41:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A25",
      "54G20",
      "54D30",
      "54A10"
    ],
    "keywords": [
      "countable chain condition",
      "ccc subspace",
      "reflection",
      "ccc tychonoff space",
      "compact hausdorff"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}