{"paper":{"title":"Topological monoids of almost monotone injective co-finite partial selfmaps of positive integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"Ivan Chuchman, Oleg Gutik","submitted_at":"2010-06-24T20:25:12Z","abstract_excerpt":"In this paper we study the semigroup $I_\\infty^\\dnearrow(N)$ of partial co-finite almost monotone bijective transformations of the set of positive integers $\\mathbb{N}$. We show that the semigroup $I_\\infty^\\dnearrow(N)$ 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. Also we prove that every Baire topology $\\tau$ on $I_\\infty^\\dnearrow(N)$ such that $(I_\\infty^\\dnearrow(N),\\tau)$ is a semitopological semigroup is discrete, describe the closure of $(I_\\infty^\\dnearrow(N),\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4873","kind":"arxiv","version":2},"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"}