{"paper":{"title":"Direct limit topologies in the categories of topological groups and of uniform spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"Dusan Repovs, Taras Banakh","submitted_at":"2009-11-20T07:52:21Z","abstract_excerpt":"We study the topological structure of the direct limit $\\glim G_n$ of a tower of topological groups $(G_n)$ in the category of topological groups and show that under some conditions on the tower $(G_n)$ the topology of $\\glim G_n$ coincides with the topology of the direct limit $\\ulim G_n$ of the groups $G_n$ endowed with the Roelcke uniformity in the category of uniform spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3985","kind":"arxiv","version":2},"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"}