{
  "annotation_id": "6e9e28dc-ec4f-4879-a588-87c7de85b359",
  "date_created": "2026-02-17T05:53:08.768000Z",
  "date_modified": "2026-02-17T05:53:08.768000Z",
  "file_hash": "2498b2a0185cfc0d629d2afc9a04a1452ae360e2ee5e19df08d35ea5637b3dc4",
  "private": false,
  "record": {
    "abstract": "We investigate the existence of compact Hausdorff spaces $X$ that are minimum with respect to $cX=K$ for some fixed covering operator $c$ and compact Hausdorff space $K$ with $cK=K$. Then, using the Yosida representation theorem, we show how that situation relates to the existence of Archimedean vector lattices $A$ with distinguished strong unit that are minimum with respect to $hA=H$ for some fixed hull operator $h$ and vector lattice $H$ with $hH=H$. Among others, we obtain answers for $c=g$ (the Gleason covering operator), $c=qF$ (the quasi-$F$ covering operator), $h = u$ (the uniform completion operator), and $h=e$ (the essential completion operator).",
    "arxiv_id": "2601.06310",
    "authors": [
      "R. E. Carrera",
      "A. W. Hager",
      "B. Wynne"
    ],
    "categories": [
      "math.FA",
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Some minimum topological spaces, and vector lattices",
    "url": "https://arxiv.org/abs/2601.06310",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "86c457d0-3f21-47bf-9716-1c037b087eea",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}