{"paper":{"title":"The $\\kappa$-Fr\\'{e}chet--Urysohn property for locally convex spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GN","authors_text":"S. Gabriyelyan","submitted_at":"2018-12-25T21:11:39Z","abstract_excerpt":"A topological space $X$ is $\\kappa$-Fr\\'{e}chet--Urysohn if for every open subset $U$ of $X$ and every $x\\in \\overline{U}$ there exists a sequence in $ U$ converging to $x$. We prove that every $\\kappa$-Fr\\'{e}chet--Urysohn Tychonoff space $X$ is Ascoli. We apply this statement and some of known results to characterize the $\\kappa$-Fr\\'echet--Urysohn property in various important classes of locally convex spaces. In particular, answering a question posed in [7] we obtain that $C_p(X)$ is Ascoli iff $X$ has the property $(\\kappa)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10166","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"}