{
  "id": "1504.04554",
  "version": "v1",
  "published": "2015-04-17T16:21:31.000Z",
  "updated": "2015-04-17T16:21:31.000Z",
  "title": "On the weak and pointwise topologies in function spaces",
  "authors": [
    "Mikołaj Krupski"
  ],
  "categories": [
    "math.FA",
    "math.GN"
  ],
  "abstract": "For a compact space $K$ we denote by $C_w(K)$ ($C_p(K)$) the space of continuous real-valued functions on $K$ endowed with the weak (pointwise) topology. In this paper we address the following basic question which seems to be open: Suppose that $K$ is an infinite (metrizable) compact space. Is it true that $C_w(K)$ and $C_p(K)$ are homeomorphic? We show that the answer is \"no\", provided $K$ is an infinite compact metrizable $C$-space. In particular our proof works for any infinite compact metrizable finite-dimemsional space $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-17T16:21:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E10",
      "54C35"
    ],
    "keywords": [
      "function spaces",
      "pointwise topologies",
      "compact space",
      "infinite compact metrizable finite-dimemsional space",
      "basic question"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150404554K"
    }
  }
}