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Gutik, Oleg; Repovš, Dušan
Georgian mathematical journal, 09/2012, Volume: 19, Issue: 3Journal Article
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.
