{"paper":{"title":"Minimal universal metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"E. Petrov, M. Kucukaslan, O. Dovgoshey, V. Bilet","submitted_at":"2015-03-02T19:22:08Z","abstract_excerpt":"Let $\\mathfrak{M}$ be a class of metric spaces. A metric space $Y$ is minimal $\\mathfrak{M}$-universal if every $X\\in\\mathfrak{M}$ can be isometrically embedded in $Y$ but there are no proper subsets of $Y$ satisfying this property. We find conditions under which, for given metric space $X$, there is a class $\\mathfrak{M}$ of metric spaces such that $X$ is minimal $\\mathfrak{M}$-universal. We generalize the notion of minimal $\\mathfrak{M}$-universal metric space to notion of minimal $\\mathfrak{M}$-universal class of metric spaces and prove the uniqueness, up to an isomorphism, for these classe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00667","kind":"arxiv","version":3},"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"}