{"paper":{"title":"The Left, the Right and the Sequential Topology on Boolean Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Aleksandar Pavlovi\\'c, Milo\\v{s} S. Kurili\\'c","submitted_at":"2018-09-26T15:09:39Z","abstract_excerpt":"For the algebraic convergence $\\lambda_{\\mathrm{s}}$, which generates the well known sequential topology $\\tau_s$ on a complete Boolean algebra ${\\mathbb B}$, we have $\\lambda_{\\mathrm{s}}=\\lambda_{\\mathrm{ls}}\\cap \\lambda_{\\mathrm{li}}$, where the convergences $\\lambda_{\\mathrm{ls}}$ and $\\lambda_{\\mathrm{li}}$ are defined by $\\lambda_{\\mathrm{ls}}(x)=\\{ \\limsup x\\}\\!\\uparrow$ and $\\lambda_{\\mathrm{li}}(x)=\\{ \\liminf x\\}\\!\\downarrow$ (generalizing the convergence of sequences on the Alexandrov cube and its dual). We consider the minimal topology $\\mathcal{O}_{\\mathrm{lsi}}$ extending the (uni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10051","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"}