{"paper":{"title":"$\\mathfrak G$-bases in free (locally convex) topological vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.LO"],"primary_cat":"math.GN","authors_text":"Arkady Leiderman, Taras Banakh","submitted_at":"2016-06-06T22:37:58Z","abstract_excerpt":"We characterize topological (and uniform) spaces whose free (locally convex) topological vector spaces have a local $\\mathfrak G$-base. A topological space $X$ has a local $\\mathfrak G$-base if every point $x$ of $X$ has a neighborhood base $(U_\\alpha)_{\\alpha\\in\\omega^\\omega}$ such that $U_\\beta\\subset U_\\alpha$ for all $\\alpha\\le\\beta$ in $\\omega^\\omega$. To construct $\\mathfrak G$-bases in free topological vector spaces, we exploit a new description of the topology of a free topological vector space over a topological (or more generally, uniform) space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01967","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"}