{"paper":{"title":"Sequential Definitions of Connectedness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Huseyin Cakalli","submitted_at":"2011-05-11T14:22:26Z","abstract_excerpt":"A topological group $X$ is called connected if the only subsets which are both open and closed are the whole space $X$ and the null set $\\emptyset$. A subset of a topological group is connected if the subspace is connected. We say that a subset $A$ of $X$ is $G$-sequentially connected if the only subsets of $A$ which are both $G$-sequentially open and $G$-sequentially closed, with respect to the relative $G$-sequentially open and $G$-sequentially closed subsets of $A$, are open and closed subsets of $A$ are $A$ and the null set, $\\emptyset$. We investigate the impact of changing the definition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2203","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"}