{
  "abstract": "Let $1<s\\le2$ and let $H_{s}[0,1]$ consist of the real-valued continuous functions on $[0,1]$ whose graphs have Hausdorff dimension $s$. We prove that every finite-dimensional subspace $E\\subset C[0,1]$ with $E\\setminus\\{0\\}\\subset H_{s}[0,1]$ is contained in a closed complemented subspace isomorphic to $c_0$, all of whose nonzero elements still belong to $H_{s}[0,1]$. This settles a question of Liu, Shi and Zhang. We also obtain the exact criterion: $H_{s}[0,1]$ is $(α,\\mathfrak{c})$-spaceable precisely when $α$ is finite. We also show that every admissible finite-dimensional subspace is contained in a dense subspace of Hamel dimension $\\mathfrak{c}$ whose nonzero elements have the same prescribed graph dimension. This also recovers maximal pointwise dense-lineability of $H_{s}[0,1]$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15992",
  "author_total": 2,
  "authors": [
    {
      "name": "Anselmo Raposo Junior"
    },
    {
      "name": "Daniel Pellegrino"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1trehhsk9thyj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15992",
  "fulltext_url": null,
  "id": "1trehhsk9thyj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15992",
  "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": "W7221824922",
  "pdf_url": "https://arxiv.org/pdf/2610.15992",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1trehhsk9thyj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15992",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15992"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$(α,\\mathfrak{c})$-spaceability of continuous functions with prescribed Hausdorff graph dimension",
  "title_text": "(α,c)-spaceability of continuous functions with prescribed Hausdorff graph dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1trehhsk9thyj",
  "venue": "arXiv",
  "versions": []
}