{"paper":{"title":"On semitopological bicyclic extensions of linearly ordered groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Kateryna Maksymyk, Oleg Gutik","submitted_at":"2016-08-02T19:44:47Z","abstract_excerpt":"For a linearly ordered group $G$ let us define a subset $A\\subseteq G$ to be a \\emph{shift-set} if for any $x,y,z\\in A$ with $y < x$ we get $x\\cdot y^{-1}\\cdot z\\in A$. We describe the natural partial order and solutions of equations on the semigroup $\\mathscr{B}(A)$ of shifts of positive cones of $A$. We study topologizations of the semigroup $\\mathscr{B}(A)$. In particular, we show that for an arbitrary countable linearly ordered group $G$ and a non-empty shift-set $A$ of $G$ every Baire shift-continuous $T_1$-topology $\\tau$ on $\\mathscr{B}(A)$ is discrete. Also we prove that for an arbitra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00959","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"}