{
  "abstract": "We prove that there are exactly $2^\\mathfrak{c}$ simultaneously bireflective and bicoreflective subconstructs of $\\mathbf{FTS}$. By the Lowen--Wuyts bijection, these correspond to the total fuzzy topologies contained in $M$, the fuzzy topology consisting of all nondecreasing left-continuous self-maps of the unit interval. The upper bound follows from a cardinality estimate. The matching lower bound is obtained by encoding $2^{\\mathfrak c}$ ultrafilters on $\\mathbb N$ into total fuzzy topologies contained in $M$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35876",
  "author_total": 1,
  "authors": [
    {
      "name": "Gao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18stmx8pr5r8t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35876",
  "fulltext_url": null,
  "id": "18stmx8pr5r8t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35876",
  "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.GM"
    ],
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7224095677",
  "pdf_url": "https://arxiv.org/pdf/2610.35876",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/18stmx8pr5r8t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.35876",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35876"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GM",
      "subfield": "general"
    }
  ],
  "title": "There Are Exactly $2^\\mathfrak{c}$ Simultaneously Bireflective and Bicoreflective Subconstructs of $\\mathbf{FTS}$",
  "title_text": "There Are Exactly 2^c Simultaneously Bireflective and Bicoreflective Subconstructs of FTS",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/18stmx8pr5r8t",
  "venue": "arXiv",
  "versions": []
}