{
  "abstract": "We lift Mundici's equivalence between MV-algebras and abelian $\\ell$-groups with a strong unit to the topological setting. To this end, we prove that, for every topological MV-algebra, the associated Mundici group can be endowed with a topology that extends the topology of the MV-algebra and makes it into an abelian topological $\\ell$-group. Among such topologies there is a finest one; we identify this topology as the topological-group reflection of the bounded-stage final topology, and construct an explicit zero-neighbourhood base in terms of the original MV-algebra topology. Using this topology, we establish a topological Mundici adjunction that restricts to an equivalence between topological MV-algebras and Mundici-fine abelian topological $\\ell$-groups with a strong unit. Here, Mundici-fine means that the group topology is the finest $\\ell$-group extension of its unit-interval topology. We also identify extremal $\\ell$-group extensions under additional hypotheses, and establish a quasitopological correspondence clarifying the distinction between separate and joint continuity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05786",
  "author_total": 3,
  "authors": [
    {
      "name": "Yifan Meng"
    },
    {
      "name": "Lili Shen"
    },
    {
      "name": "Dexue Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7m46zaesdr5fs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05786",
  "fulltext_url": null,
  "id": "7m46zaesdr5fs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05786",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05786",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7m46zaesdr5fs.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05786",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05786"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A topological Mundici representation theorem",
  "title_text": "A topological Mundici representation theorem",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:29Z",
  "url": "https://research.draconitic.com/paper/7m46zaesdr5fs",
  "venue": "arXiv",
  "versions": []
}