{"paper":{"title":"Topologies on groups determined by sets of convergent sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"S. S. Gabriyelyan","submitted_at":"2011-01-14T10:06:06Z","abstract_excerpt":"A Hausdorff topological group $(G,\\tau)$ is called an $s$-group and $\\tau$ is called an $s$-topology if there is a set $S$ of sequences in $G$ such that $\\tau$ is the finest Hausdorff group topology on $G$ in which every sequence of $S$ converges to the unit. The class $\\mathbf{S}$ of all $s$-groups contains all sequential Hausdorff groups and it is finitely multiplicative. A quotient group of an $s$-group is an $s$-group. For a non-discrete topological group $(G,\\tau)$ the following three assertions are equivalent: 1) $(G,\\tau)$ is an $s$-group, 2) $(G,\\tau)$ is a quotient group of a Graev fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2754","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"}