{"paper":{"title":"Topological structure of non-separable sigma-locally compact convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GT","authors_text":"I.Banakh, K.Koshino, T.Banakh","submitted_at":"2013-05-07T15:24:21Z","abstract_excerpt":"For an infinite cardinal $\\kappa$ let $\\ell_2(\\kappa)$ be the linear hull of the standard othonormal base of the Hilbert space $\\ell_2(\\kappa)$ of density $\\kappa$. We prove that a non-separable convex subset $X$ of density $\\kappa$ in a locally convex linear metric space if homeomorphic to the space (i) $\\ell_2^f(\\kappa)$ if and only if $X$ can be written as countable union of finite-dimensional locally compact subspaces, (ii) $[0,1]^\\omega\\times \\ell_2^f(\\kappa)$ if and only if $X$ contains a topological copy of the Hilbert cube and $X$ can be written as a countable union of locally compact "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1557","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"}