{"paper":{"title":"Topological monoids of monotone injective partial selfmaps of $\\mathbb{N}$ with cofinite domain and image","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"Du\\v{s}an Repov\\v{s}, Oleg Gutik","submitted_at":"2011-08-14T07:39:15Z","abstract_excerpt":"In this paper we study the semigroup $\\mathscr{I}_{\\infty}^{\\nearrow}(\\mathbb{N})$ of partial cofinal monotone bijective transformations of the set of positive integers $\\mathbb{N}$. We show that the semigroup $\\mathscr{I}_{\\infty}^{\\nearrow}(\\mathbb{N})$ has algebraic properties similar to the bicyclic semigroup: it is bisimple and all of its non-trivial group homomorphisms are either isomorphisms or group homomorphisms. We also prove that every locally compact topology $\\tau$ on $\\mathscr{I}_{\\infty}^{\\nearrow}(\\mathbb{N})$ such that $(\\mathscr{I}_{\\infty}^{\\nearrow}(\\mathbb{N}),\\tau)$ is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2848","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"}