{"paper":{"title":"Symmetric inverse topological semigroups of finite rank $\\leqslant n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andriy Reiter, Oleg Gutik","submitted_at":"2009-12-01T16:32:47Z","abstract_excerpt":"We study topological properties of the symmetric inverse topological semigroup of finite transformations $\\mathscr{I}_\\lambda^n$ of the rank $\\leqslant n$. We show that the topological inverse semigroup $\\mathscr{I}_\\lambda^n$ is algebraically $h$-closed in the class of topological inverse semigroups. Also we prove that a topological semigroup $S$ with countably compact square $S\\times S$ does not contain the semigroup $\\mathscr{I}_\\lambda^n$ for infinite cardinal $\\lambda$ and show that the Bohr compactification of an infinite topological symmetric inverse semigroup of finite transformations "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0198","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"}