{"paper":{"title":"Order Topology and Frink Ideal Topology of Effect Algebras","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Lei Qiang, Li Ronglu, Wu Junde","submitted_at":"2009-08-24T01:11:08Z","abstract_excerpt":"In this paper, the following results are proved: (1) $ $ If $E$ is a complete atomic lattice effect algebra, then $E$ is (o)-continuous iff $E$ is order-topological iff $E$ is totally order-disconnected iff $E$ is algebraic. (2) $ $ If $E$ is a complete atomic distributive lattice effect algebra, then its Frink ideal topology $\\tau_{id}$ is Hausdorff topology and $\\tau_{id}$ is finer than its order topology $\\tau_{o}$, and $\\tau_{id}=\\tau_o$ iff 1 is finite iff every element of $E$ is finite iff $\\tau_{id}$ and $\\tau_o$ are both discrete topologies. (3) $ $ If $E$ is a complete (o)-continuous "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3350","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}