{
  "abstract": "Let $\\mathcal{F}^{m}=\\{A\\subset[m]\\}$, endowed with the symmetric difference metric and the Cardinality Reverse-Lexicographic order. That way, we compute the homotopy type $\\operatorname{Čech}\\left(\\mathcal{F}_{\\preceq a}^m; \\frac{r}{2}=1\\right)$ by relating it to consecutively adding vertices of $\\mathbb{I}^m$, the unit hypercube of $m$th dimension, to point $0$. Further, for higher $r$, we propose a conjecture regarding contractibility of a subcomplex implying a formula for the exact number of wedges of $\\mathbb{S}^ 3$'s and $\\mathbb{S}^ 4$'s in the $\\operatorname{Čech}$ complex.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32786",
  "author_total": 1,
  "authors": [
    {
      "name": "Anamitro Biswas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eafbv6fy0xkfr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32786",
  "fulltext_url": null,
  "id": "eafbv6fy0xkfr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32786",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7214753129",
  "pdf_url": "https://arxiv.org/pdf/2609.32786",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eafbv6fy0xkfr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32786",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32786"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Čech complexes for finite sets",
  "title_text": "Čech complexes for finite sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/eafbv6fy0xkfr",
  "venue": "arXiv",
  "versions": []
}