On monoids of monotone injective partial selfmaps of integers with cofinite domains and images
Олег Гутік, Dusan D. Repovs · Georgian Mathematical Journal · 2012
We study the semigroup of monotone injective partial selfmaps of the set of integers having cofinite domain and image. We show that is bisimple and all of its non-trivial semigroup homomorphisms are either isomorphisms or group homomorphisms. We also prove that every Baire topology on , such that is a Hausdorff semitopological semigroup, is discrete and we construct a non-discrete Hausdorff inverse semigroup topology on . We show that the discrete semigroup cannot be embedded into some classes of compact-like topological semigroups and that its remainder under the closure in a topological semigroup S is an ideal in S .