{
  "annotation_id": "c87d7fd4-a34f-4bc0-bd19-7d37b325c6ce",
  "date_created": "2026-03-02T18:02:06.636000Z",
  "date_modified": "2026-03-02T18:02:06.636000Z",
  "file_hash": "d982977d4a43158cf1b9dfcabeb901cb3ef1ff9e51c8ac07f2c1dd179795e1d0",
  "private": false,
  "record": {
    "abstract": "We initiate a study of topological orthoalgebras (TOAs), concentrating on the\ncompact case. Examples of TOAs include topological orthomodular lattices, and\nalso the projection lattice of a Hilbert space. As the latter example\nillustrates, a lattice-ordered TOA need not be a topological lattice. However,\nwe show that a compact Boolean TOA is a topological Boolean algebra. Using\nthis, we prove that any compact regular TOA is atomistic, and has a compact\ncenter. We prove also that any compact TOA with isolated 0 is of finite height.\nWe then focus on stably ordered TOAs: those in which the upper-set generated by\nan open set is open. These include both topological orthomodular lattices and\ninterval orthoalgebras -- in particular, projection lattices. We show that the\ntopology of a compact stably-ordered TOA with isolated 0 is determined by that\nof of its space of atoms.",
    "arxiv_id": "quant-ph/0405180",
    "authors": [
      "Alexander Wilce"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Compact Orthoalgebras",
    "url": "https://arxiv.org/abs/quant-ph/0405180"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ddf1dccc-e210-4ee8-ba83-4de3c64b3cf3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}