{"paper":{"title":"Sequential coarse structures of topological groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Igor Protasov","submitted_at":"2019-03-10T17:09:59Z","abstract_excerpt":"We endow a topological group $(G, \\tau)$ with a coarse structure defined by the smallest group ideal $S_{\\tau} $ on $G$ containing all converging sequences with their limits and denote the obtained coarse group by $(G, S_{\\tau})$. If $G$ is discrete then $(G, S_{\\tau})$ is a finitary coarse group studding in Geometric Group Theory. The main result: if a topological abelian group $(G, \\tau)$ contains a non-trivial converging sequence then $asdim \\ (G, S_{\\tau})= \\infty $."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04915","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"}