{
  "id": "1904.04906",
  "version": "v1",
  "published": "2019-04-09T20:52:32.000Z",
  "updated": "2019-04-09T20:52:32.000Z",
  "title": "Countable dense homogeneity of function spaces",
  "authors": [
    "Rodrigo Hernández-Gutiérrez"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper we consider the question of when the space $C_p(X)$ of continuous real-valued functions on $X$ with the pointwise convergence topology is countable dense homogeneous. In particular, we focus on the case when $X$ is countable with a unique non-isolated point $\\infty$. In this case, $C_p(X)$ is countable dense homogeneous if and only if the filter of open neighborhoods of $\\infty$ is a non-meager $P$-filter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-09T20:52:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D80",
      "54A35",
      "54C35"
    ],
    "keywords": [
      "countable dense homogeneity",
      "function spaces",
      "countable dense homogeneous",
      "open neighborhoods",
      "unique non-isolated point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}