{"paper":{"title":"Oscillation of Urysohn type spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Norbert Sauer","submitted_at":"2012-03-24T20:38:15Z","abstract_excerpt":"A metric space $\\mathrm{M}=(M;\\de)$ is {\\em homogeneous} if for every isometry $\\alpha$ of a finite subspace of $\\mathrm{M}$ to a subspace of $\\mathrm{M}$ there exists an isometry of $\\mathrm{M}$ onto $\\mathrm{M}$ extending $\\alpha$. The metric space $\\mathrm{M}$ is {\\em universal} if it isometrically embeds every finite metric space $\\mathrm{F}$ with $\\dist(\\mathrm{F})\\subseteq \\dist(\\mathrm{M})$. ($\\dist(\\mathrm{M})$ being the set of distances between points of $\\mathrm{M}$.)\n  A metric space $\\mathrm{M}$ is {\\em oscillation stable} if for every $\\epsilon>0$ and every uniformly continuous an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6024","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"}