{
  "abstract": "Given a metric space $Y$ and a compact subspace $X$, we present a method for constructing an inverse sequence of finite topological spaces by sampling points from neighborhoods of $X$ in $Y$. We show that these inverse sequences can be employed to define shape theory and to approximate shape invariants, such as Čech homology groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34328",
  "author_total": 1,
  "authors": [
    {
      "name": "Pedro J. Chocano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0np4qpqmmydh9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34328",
  "fulltext_url": null,
  "id": "0np4qpqmmydh9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34328",
  "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.GN"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.34328",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0np4qpqmmydh9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34328",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34328"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "From samples to shape: a finite approach to topological invariants",
  "title_text": "From samples to shape: a finite approach to topological invariants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/0np4qpqmmydh9",
  "venue": "arXiv",
  "versions": []
}