{"paper":{"title":"Metric products and continuation of isotone functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"E. Petrov, G. Kozub, O. Dovgoshey","submitted_at":"2012-03-01T18:00:31Z","abstract_excerpt":"Let $\\mathbb{R}_+=[0,\\infty)$ and let $A\\subseteq\\mathbb{R}^n_+$. We have found the necessary and sufficient conditions under which a function $\\Phi:A\\to\\mathbb{R}_+$ has an isotone subadditive continuation on $\\mathbb{R}^n_+$. It allows us to describe the metrics, defined on the Cartesian product $X_1\\times...\\times X_n$ of given metric spaces $(X_1,d_{X_1}),...,(X_n,...,d_{X_n})$, generated by the isotone metric preserving functions on $\\mathbb{R}^n_+$. It also shows that the isotone metric preserving functions $\\Phi:\\mathbb{R}^n_+\\to\\mathbb{R}_+$ coincide with the first moduli of continuity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0257","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"}