{"paper":{"title":"Topologies on spaces of valuations: a closeness criterion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.AC","authors_text":"Josnei Novacoski","submitted_at":"2015-09-21T19:31:39Z","abstract_excerpt":"This paper is part of a program to understand topologies on spaces of valuations. We fix an ordered abelian group $\\Gamma$ and an integral domain $R$. We study the relation between a topology on $\\Gamma_\\infty$ and the induced topology on the set $\\mathcal W_\\Gamma$ of all valuations of $R$ taking values in $\\Gamma_\\infty$. For instance, we give a criterion for $ \\mathcal W_\\Gamma$ to be closed in $\\left(\\Gamma_\\infty\\right)^R$. We also discuss the effect of this criterion for natural topologies on $\\Gamma_\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06356","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"}