{"paper":{"title":"A separable Fr\\'echet space of almost universal disposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"C. Bargetz, J. Kakol, W. Kubi\\'s","submitted_at":"2016-03-21T09:19:31Z","abstract_excerpt":"The Gurari\\u{\\i} space is the unique separable Banach space $\\mathbb{G}$ which is of almost universal disposition for finite-dimensional Banach spaces, which means that for every $\\varepsilon>0$, for all finite-dimensional normed spaces $E \\subseteq F$, for every isometric embedding ${e}\\colon{E}\\to{\\mathbb{G}}$ there exists an $\\varepsilon$-isometric embedding ${f}\\colon{F}\\to{\\mathbb{G}}$ such that $f \\restriction E = e$.\n  We show that $\\mathbb{G}^{\\mathbb{N}}$ with a special sequence of semi-norms is of almost universal disposition for finite-dimensional graded Fr\\'echet spaces. The constr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06361","kind":"arxiv","version":1},"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"}