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Journal of Applied Sciences
  Year: 2010 | Volume: 10 | Issue: 9 | Page No.: 766-771
DOI: 10.3923/jas.2010.766.771
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Congruences on Topological S-Acts and Topological Semigroups

Behnam Khosravi

Let (S, τS) be a topological semigroup. In this note, we study the notion of topological congruences on topological S-acts, i.e., for a topological S-act (A, τ), when A/θ with the quotient topology is a topological S-act. Let (A, τ) be a topological S-act (S-flow) and θ be an S-act congruence on A (a semigroup congruence on S) and let Lθ be the lattice of closed subsets, relative to the closure operator Cθ. As the main result of this study, we prove that θ is a topological congruence on (A, τA) (resp., (S, τS)) if and only if (A, τA ∩ Lθ) (resp., (S, τS ∩ Lθ)) is a topological S-act (a topological semigroup). Also, we prove that when Y is closed, the study of Rees congruence ρY is related to the study of the lattice of open sets which contain Y.
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How to cite this article:

Behnam Khosravi , 2010. Congruences on Topological S-Acts and Topological Semigroups. Journal of Applied Sciences, 10: 766-771.

DOI: 10.3923/jas.2010.766.771






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