{
  "id": "1312.6081",
  "version": "v1",
  "published": "2013-12-20T19:21:18.000Z",
  "updated": "2013-12-20T19:21:18.000Z",
  "title": "A note on condensations of function spaces onto $σ$-compact and analytic spaces",
  "authors": [
    "Mikołaj Krupski"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "Modifying a construction of W. Marciszewski we prove (in ZFC) that there exists a subspace of the real line $\\mathbb{R}$, such that the realcompact space $C_p(X)$ of continuous real-valued functions on $X$ with the pointwise convergence topology does not admit a continuous bijection onto a $\\sigma$-compact space. This answers a question of Arhangel'skii.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-20T19:21:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C35",
      "54A10",
      "54D60"
    ],
    "keywords": [
      "function spaces",
      "analytic spaces",
      "condensations",
      "pointwise convergence topology",
      "realcompact space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.6081K"
    }
  }
}