Subscribe Now Subscribe Today
Science Alert
 
Blue
   
Curve Top
Journal of Applied Sciences
  Year: 2010 | Volume: 10 | Issue: 9 | Page No.: 766-771
DOI: 10.3923/jas.2010.766.771
 
Facebook Twitter Digg Reddit Linkedin StumbleUpon E-mail

Congruences on Topological S-Acts and Topological Semigroups

Behnam Khosravi

Abstract:
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.
PDF Fulltext XML References Citation Report Citation
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

URL: https://scialert.net/abstract/?doi=jas.2010.766.771

COMMENT ON THIS PAPER
 
 
 

 

 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 

Curve Bottom