{
  "abstract": "We prove that every continuous homomorphism from a complete topologized semilattice to a Hausdorff semitopological semilattice has closed image, answering a question of Banakh and Bardyla. The main step is the convergence of idempotent ultrafilters on complete semitopological semilattices. We also prove that, for every complete subsemilattice $X$ of a Hausdorff semitopological semilattice $Y$, the natural order of $X$ is closed in $Y\\times Y$. In particular, the natural order of every complete Hausdorff semitopological semilattice $X$ is closed in $X\\times X$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01545",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexander V. Osipov"
    },
    {
      "name": "Konstantin Kazachenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5wegen4b5dc74.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01545",
  "fulltext_url": null,
  "id": "5wegen4b5dc74",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01545",
  "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"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01545",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5wegen4b5dc74.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01545",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01545"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Idempotent Ultrafilters and Closed Images of Complete Semilattices",
  "title_text": "Idempotent Ultrafilters and Closed Images of Complete Semilattices",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/5wegen4b5dc74",
  "venue": "arXiv",
  "versions": []
}