{
  "abstract": "We show that for a broad class of spaces $X$, the space $C_p(X)$ of continuous real-valued functions on $X$ equipped with the pointwise topology maps bijectively onto any separable infinite-dimensional Banach space with the weak topology. We prove that the inverse $φ^{-1}$ of any continuous bijection $φ: C_p(X)\\to (E,w)$, where $X$ is an arbitrary infinite Tychonoff space and $(E,w)$ is an arbitrary normed space with the weak topology, is everywhere discontinuous. This generalizes a recent result of Kania--Kąkol and solves a problem raised by Kąkol, Leiderman and Michalak by providing a complete classification of function spaces $C_p(X)$ that are homeomorphic to Banach spaces with the weak topology.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24165",
  "author_total": 2,
  "authors": [
    {
      "name": "Mikołaj Krupski"
    },
    {
      "name": "Witold Marciszewski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7np15bph2get9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24165",
  "fulltext_url": null,
  "id": "7np15bph2get9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24165",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7223067857",
  "pdf_url": "https://arxiv.org/pdf/2610.24165",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7np15bph2get9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24165",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24165"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On condensations of $C_p(X)$ spaces onto Banach spaces with the weak topology",
  "title_text": "On condensations of C_p(X) spaces onto Banach spaces with the weak topology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/7np15bph2get9",
  "venue": "arXiv",
  "versions": []
}