Topological monoids of almost monotone injective co-finite partial selfmaps of the set of positive integers - Chuchman, I.Ya.; Gutik, O.V. (Carpathian Mathematical Publications, 2010)
In this paper we study the semigroup I_∞^ \!\!\! earrow(N) of partial co-finite almost monotone bijective transformations of the set of positive integers N. We show that the semigroup I_∞^ \!\!\! earrow(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 τ on I_∞^ \!\!\! earrow(N) such that (I_∞^ \!\!\! earrow(N),τ) is a semitopological semigroup is discrete, describe the closure of (I_∞^ \!\!\! earrow(N),τ) in a topological semigroup and construct non-discrete Hausdorff semigroup topologies on I_∞^ \!\!\! earrow(N).