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On monoids of monotone injective partial selfmaps of integers with cofinite domains and images
-
Oleg Gutik
and
Dušan Repovš
Published/Copyright:
September 18, 2012
Abstract.
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.
Keywords: Topological semigroup; semitopological semigroup; semigroup of bijective partial transformations; symmetric inverse
semigroup; ideal; Baire space; semigroup topologization; bicyclic semigroup
Received: 2011-04-26
Revised: 2012-04-01
Published Online: 2012-09-18
Published in Print: 2012-09-01
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- The Plemelj–Privalov theorem in variable exponent Clifford analysis
- Almost everywhere convergence of a subsequence of logarithmic means of Fourier series on the group of 2-adic integers
- Identities and generating functions on Chebyshev polynomials
- Left annihilators of power values of commutators with generalized derivations
- On various classes of bitopological spaces
- On P-torsion modules over a pullback of two Dedekind domains
- A remark on a polynomial matrix factorization theorem
- Convergence of double Fourier series and generalized Λ-variation
- On monoids of monotone injective partial selfmaps of integers with cofinite domains and images
- On the boundedness of product kernel operators with measures
- A new class of generalized Hermite–Bernoulli polynomials
- Global nonexistence and stability of solutions of inverse problems for a class of Petrovsky systems
- Comment on the sums
