{"paper":{"title":"Metrizability of minimal and unbounded topologies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marko Kandi\\'c, Mitchell A. Taylor","submitted_at":"2017-09-15T21:06:51Z","abstract_excerpt":"In 1987, I. Labuda proved a general representation theorem that, as a special case, shows that the topology of local convergence in measure is the minimal topology on Orlicz spaces and $L_{\\infty}$. Minimal topologies connect with the recent, and actively studied, subject of \"unbounded convergences\". In fact, a Hausdorff locally solid topology $\\tau$ on a vector lattice $X$ is minimal iff it is Lebesgue and the $\\tau$ and unbounded $\\tau$-topologies agree. In this paper, we study metrizability, submetrizability, and local boundedness of the unbounded topology, $u\\tau$, associated to $\\tau$ on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05407","kind":"arxiv","version":1},"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"}