{"paper":{"title":"The semigroup of monotone co-finite partial homeomorphisms of the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Kateryna Melnyk, Oleg Gutik","submitted_at":"2019-04-14T07:59:00Z","abstract_excerpt":"In the paper we investigate the semigroup of monotone co-finite partial homeomorphisms of the space of the usual real line $\\mathbb{R}$. We prove that the inverse semigroup $\\mathscr{P\\!\\!H}^+_{\\!\\!\\operatorname{\\textsf{cf}}}\\!(\\mathbb{R})$ is factorizable and $F$-inverse. We describe the structure of the band of the semigroup $\\mathscr{P\\!\\!H}^+_{\\!\\!\\operatorname{\\textsf{cf}}}\\!(\\mathbb{R})$, its two-sided ideals, maximal subgroups and Green's relations. We prove that the quotient semigroup $\\mathscr{P\\!\\!H}^+_{\\!\\!\\operatorname{\\textsf{cf}}}\\!(\\mathbb{R})/\\mathfrak{C}_{\\textsf{mg}}$, where "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06647","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"}