{
  "abstract": "Wilker-type properties record how a compact set can be split along a binary open cover, and they are precisely the continuity conditions for the union operation on open lattices, governing the topology of power and function spaces. We give a unified treatment of the four properties $\\W$, $\\Ww$, $\\Wi$ and $\\Win$. We prove that $\\Wi$ and $\\Win$ are hereditary for arbitrary subspaces, whereas $\\W$ and $\\Ww$ are hereditary only for closed subspaces; all four are preserved by continuous retracts, and $\\Ww$, $\\Wi$, $\\Win$ are finitely additive over topological sums. For KC-spaces $\\Ww$ and $\\Wi$ coincide, and spaces whose compact subspaces are Hausdorff belong to $\\Win$. Using Kovár's compact KC-space $M_0$ and its variant $\\QQ^{+}$, we obtain countably infinite compact KC-spaces in $\\Wi\\setminus\\W$, showing $\\Wi$ is strictly weaker than $\\W$. Conversely, we construct compact $T_1$ spaces whose product fails $\\Ww$, proving the classes $\\Ww$ and $\\Wi$ are not reflective. We further show Vietoris constructions need not preserve $\\Wi$, and prove that $\\Ok(M_0)\\cong \\Ck(M_0,\\Sier)$ is not sober and fails property~$S$. Open problems are collected at the end.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06060",
  "author_total": 2,
  "authors": [
    {
      "name": "Wu Wang"
    },
    {
      "name": "Jiajun Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fh7rcvr2reb3v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06060",
  "fulltext_url": null,
  "id": "fh7rcvr2reb3v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06060",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GN"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06060",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fh7rcvr2reb3v.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06060",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06060"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On Wilker-Type Properties",
  "title_text": "On Wilker-Type Properties",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/fh7rcvr2reb3v",
  "venue": "arXiv",
  "versions": []
}