{"paper":{"title":"On rectifiable spaces and paratopological groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"Fucai Lin, Rongxin Shen","submitted_at":"2011-10-01T07:25:19Z","abstract_excerpt":"We mainly discuss the cardinal invariants and generalized metric properties on paratopological groups or rectifiable spaces, and show that: (1) If $A$ and $B$ are $\\omega$-narrow subsets of a paratopological group $G$, then $AB$ is $\\omega$-narrow in $G$, which give an affirmative answer for \\cite[Open problem 5.1.9]{A2008}; (2) Every bisequential or weakly first-countable rectifiable space is metrizable; (3) The properties of Fr$\\acute{e}$chet-Urysohn and strongly Fr$\\acute{e}$chet-Urysohn are coincide in rectifiable spaces; (4) Every rectifiable space $G$ contains a (closed) copy of $S_{\\ome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0082","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"}