{
  "abstract": "We study ball-covering properties in Lipschitz-free spaces. We establish an extension criterion for proving that $\\mathcal F(M)$ fails the ball-covering property and apply it to several classes of nonseparable metric spaces. In contrast, we construct a nonseparable uniformly discrete metric space $M$ such that $\\mathcal F(M)$ has the uniform ball-covering property and is isomorphic to $\\ell_1(2^ω)$. More precisely, $\\mathcal F(M)$ has the $α$-ball-covering property for every $α\\in[-1,1)$. This example also shows that these quantitative ball-covering properties are not hereditary within the class of Lipschitz-free spaces. Finally, we prove some stability results under sufficiently small bi-Lipschitz perturbations of the metric.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27485",
  "author_total": 4,
  "authors": [
    {
      "name": "Ramón J. Aliaga"
    },
    {
      "name": "Colin Petitjean"
    },
    {
      "name": "Antonín Procházka"
    },
    {
      "name": "Daniele Puglisi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ansf56mj40mn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27485",
  "fulltext_url": null,
  "id": "2ansf56mj40mn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27485",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7214233898",
  "pdf_url": "https://arxiv.org/pdf/2609.27485",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ansf56mj40mn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27485",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27485"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Ball-Covering Property in Lipschitz-Free Spaces",
  "title_text": "The Ball-Covering Property in Lipschitz-Free Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/2ansf56mj40mn",
  "venue": "arXiv",
  "versions": []
}