{"paper":{"title":"Coarse structures on groups defined by $T$-sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"D. Dikranjan, I. Protasov","submitted_at":"2019-02-06T18:30:59Z","abstract_excerpt":"A sequence $(a_{n}) $ in an Abelian group is called a $T$-sequence if there exists a Hausdorff group topology on $G$ in which $(a_{n}) $ converges to $0$. For a $T$-sequence $(a_{n}) $, $\\tau_{(a_{n}) } $ denotes the strongest group topology on $G$ in which $(a_{n}) $ converges to $0$. The ideal $\\mathcal{I}_{(a_{n})} $ of all precompact subsets of $(G, \\tau_{(a_{n}) } )$ defines a coarse structure on $G$ with base of entourages $\\{(x, y): x-y \\in P \\}$, $P\\in\\mathcal{I}_{(a_{n})}. $ We prove that $asdim \\ \\ (G, \\mathcal{I}_{(a_{n}) }) =\\infty $ for every non-trivial $T$-sequence $(a_{n})$ on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02320","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"}