Topological monoids of almost monotone injective co-finite partial selfmaps of positive integers

Abstract

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 $(I_\infty^\dnearrow(N),τ)$ is a semitopological semigroup is discrete, describe the closure of $(I_\infty^\dnearrow(N),τ)$ in a topological semigroup and construct non-discrete Hausdorff semigroup topologies on $I_\infty^\dnearrow(N)$.

10 pages

References in corpus (1)

• Semigroup Closures of Finite Rank Symmetric Inverse Semigroups