{"paper":{"title":"Note on Archimedean property in ordered vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eduard Emelyanov","submitted_at":"2013-09-11T17:42:02Z","abstract_excerpt":"It is shown that an ordered vector space $X$ is Archimedean if and only if $\\inf\\limits_{\\tau\\in\\{\\tau\\}, y\\in L}(x_\\tau -y) \\ = 0$ for any bounded decreasing net $x_\\tau\\downarrow$ in $X$, where $L$ is the collection of all lower bounds of $\\{x_\\tau\\}_{\\tau}$. We give also a characterization of the almost Archimedean property of $X$ in terms of existence of a linear extension of an additive mapping $T:Y_+\\to X_+$ of the positive cone $Y_+$ of an ordered vector space $Y$ into $X_+$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2903","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"}