{
  "abstract": "We prove that a Lipschitz-free space $\\F(M)$ fails Kwapień's property (K) whenever its underlying metric space $M$ contains a bi-Lipschitz copy of $C\\times K$, where $C\\subset\\R$ is closed with positive measure and $K$ contains a Cantor metric space. Consequently, this holds for every subset of $\\R^n$, $n\\geqslant2$, whose closure has positive measure, and for a compact planar set of Assouad dimension one. These Lipschitz-free spaces embed into no strongly weakly compactly generated space and no $L_1$-space; in the separable case their duals are not isomorphic to $\\ell_\\infty$. Combining our result with a decomposition of Aliaga and Medina, we show that $\\F(\\R^n\\times\\Z^m)$ is strongly weakly compactly generated if and only if it has (K), and this occurs precisely when $n\\leqslant1$. In particular, $\\F(\\R^2)$ does not embed isomorphically into $\\F(\\R\\times\\Z)$, answering a question of Aliaga. The planar examples nevertheless have the Dunford--Pettis property and Pełczyński's property $(V^*)$ and are weakly sequentially complete.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36194",
  "author_total": 2,
  "authors": [
    {
      "name": "Tomasz Kania"
    },
    {
      "name": "Jerzy Kąkol"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6rsj1an2vxvvs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36194",
  "fulltext_url": null,
  "id": "6rsj1an2vxvvs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36194",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7224137305",
  "pdf_url": "https://arxiv.org/pdf/2610.36194",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6rsj1an2vxvvs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36194",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36194"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Kwapień's property (K) in Lipschitz-free spaces",
  "title_text": "Kwapień's property (K) in Lipschitz-free spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/6rsj1an2vxvvs",
  "venue": "arXiv",
  "versions": []
}