{"paper":{"title":"Topological and uniform structures on universal covering spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"A. Mitra, B. Labuz, J. Dydak, N. Brodskiy","submitted_at":"2012-06-01T03:16:09Z","abstract_excerpt":"We discuss various uniform structures and topologies on the universal covering space $\\widetilde X$ and on the fundamental group $\\pi_1(X,x_0)$. We introduce a canonical uniform structure $CU(X)$ on a topological space $X$ and use it to relate topologies on $\\widetilde X$ and uniform structures on $\\widetilde{CU(X)}$.\n  Using our concept of universal Peano space we show connections between the topology introduced by Spanier and a uniform structure of Berestovskii and Plaut. We give a sufficient and necessary condition for Berestovskii-Plaut structure to be identical with the one generated by t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0071","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"}