{"paper":{"title":"On the topologies induced by a cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mehdi Ghasemi","submitted_at":"2014-03-27T04:35:38Z","abstract_excerpt":"Let $A$ be a commutative and unital $\\mathbb{R}$-algebra, and $M$ be an Archimedean quadratic module of $A$. We define a submultiplicative seminorm $\\|\\cdot\\|_M$ on $A$, associated with $M$. We show that the closure of $M$ with respect to $\\|\\cdot\\|_M$-topology is equal to the closure of $M$ with respect to the finest locally convex topology on $A$. We also compute the closure of any cone in $\\|\\cdot\\|_M$-topology. Then we omit the Archimedean condition and show that there still exists a lmc topology associated to $M$, pursuing the same properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6913","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"}