{"paper":{"title":"On a topological simple Warne extension of a semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Iryna Fihel, Kateryna Pavlyk, Oleg Gutik","submitted_at":"2013-01-07T15:45:04Z","abstract_excerpt":"In the paper we introduce topological $\\mathbb{Z}$-Bruck-Reilly and topological $\\mathbb{Z}$-Bruck extensions of (semi)topological monoids which are generalizations of topological Bruck-Reilly and topological Bruck extensions of (semi)topological monoids and study their topologizations. The sufficient conditions under which the topological $\\mathbb{Z}$-Bruck-Reilly ($\\mathbb{Z}$-Bruck) extension admits only the direct sum topology and conditions under which the direct sum topology can be coarsened are given. Also, topological characterizations of some classes of $I$-bisimple (semi)topological "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1232","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"}