{
  "abstract": "Let $X$ be a metric space without isolated points. In this paper we prove that $E$ is a $G_δ$-set in $X$ if and only if there exists a continuous function $f:X\\to\\mathbb{R}$ whose big Lipschitz derivative is infinite precisely on $E$. To this end, we introduce a new generalization of the classical Takagi function to the setting of metric spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38856",
  "author_total": 3,
  "authors": [
    {
      "name": "Jesús Llorente"
    },
    {
      "name": "Oleksandr Maslyuchenko"
    },
    {
      "name": "Ziemowit Wójcicki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e2fykrayxtr43.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38856",
  "fulltext_url": null,
  "id": "e2fykrayxtr43",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38856",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38856",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e2fykrayxtr43.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38856",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38856"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Characterization of sets in metric spaces where the big Lipschitz derivative is infinite",
  "title_text": "Characterization of sets in metric spaces where the big Lipschitz derivative is infinite",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/e2fykrayxtr43",
  "venue": "arXiv",
  "versions": []
}