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

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

2010-06-24

arxiv.org/abs/1006.4873v2

Carpathian Mathematical Publications 2 (2010), no. 1, 119-132

Mathematics

Group Theory

10 pages

Scientific paper

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 $(I_\infty^\dnearrow(N),\tau)$ in a topological semigroup and construct non-discrete Hausdorff semigroup topologies on $I_\infty^\dnearrow(N)$.

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