{
  "abstract": "Working with tools from infinite-dimensional topology and using measure-theoretic ideas we analyze numerous well-known fami\\-lies of copu\\-las and quasi-copulas from a topological perspective, prove that most of them are homeomorphic to the Hilbert cube $\\mathcal{H}$ and hence have the Fixed Point as well as the Disjoint Cells property. Working with so-called $Z$-sets, we then study how large one set is within another. Doing so, in order to show that a set $A$ is small/topologically negligible within a compact metric space $(Ω,m)$, we construct a homeomorphism $h: [0,1] \\times \\mathcal{H} \\to Ω$ mapping $\\{0\\} \\times \\mathcal{H}$ to $A$. The obtained results are to a certain extent surprising since various supposedly small families are topologically large.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35912",
  "author_total": 3,
  "authors": [
    {
      "name": "Fabrizio Durante"
    },
    {
      "name": "Juan Fernández Sánchez"
    },
    {
      "name": "Wolfgang Trutschnig"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7cbyewpdb2wrt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35912",
  "fulltext_url": null,
  "id": "7cbyewpdb2wrt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35912",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7224135666",
  "pdf_url": "https://arxiv.org/pdf/2610.35912",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7cbyewpdb2wrt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.35912",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35912"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On families of copulas and quasi-copulas homeomorphic to the Hilbert cube and related results",
  "title_text": "On families of copulas and quasi-copulas homeomorphic to the Hilbert cube and related results",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/7cbyewpdb2wrt",
  "venue": "arXiv",
  "versions": []
}