{"paper":{"title":"The semigroup of star partial homeomorphisms of a finite deminsional Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Kateryna Melnyk, Oleg Gutik","submitted_at":"2019-05-26T06:02:43Z","abstract_excerpt":"In the paper the notion of a star partial homeomorphism of a finite dimensional Euclidean space $\\mathbb{R}^n$ is introduced. We describe the structure of the semigroup $\\mathbf{PStH}_{\\mathbb{R}^n}$ of star partial homeomorphisms of the space $\\mathbb{R}^n.$ The structure of the band of $\\mathbf{PStH}_{\\mathbb{R}^n}$ and Green's relations on $\\mathbf{PStH}_{\\mathbb{R}^n}$ are described. We show that $\\mathbf{PStH}_{\\mathbb{R}^n}$ is a bisimple inverse semigroup and every non-unit congruence on $\\mathbf{PStH}_{\\mathbb{R}^n}$ is a group congruence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10736","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"}