{"paper":{"title":"On locally compact shift-continuous topologies on the $\\alpha$-bicyclic monoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Serhii Bardyla","submitted_at":"2017-07-22T09:43:00Z","abstract_excerpt":"A topology $\\tau$ on a monoid $S$ is called {\\em shift-continuous} if for every $a,b\\in S$ the two-sided shift $S\\to S$, $x\\mapsto axb$, is continuous. For every ordinal $\\alpha\\le \\omega$, we describe all shift-continuous locally compact Hausdorff topologies on the $\\alpha$-bicyclic monoid $\\mathcal{B}_{\\alpha}$. More precisely, we prove that the lattice of shift-continuous locally compact Hausdorff topologies on $\\mathcal{B}_{\\alpha}$ is anti-isomorphic to the segment of $[1,\\alpha]$ of ordinals, endowed with the natural well-order. Also we prove that for each ordinal $\\alpha$ the $\\alpha+1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07130","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"}