Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2010.766.771KhosraviBehnam92010109Let (S, τ_{S}) 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 L_{θ }be the lattice of closed subsets, relative to the closure operator C_{θ}. As the main result of this study, we prove that θ is a topological congruence on (A, τ_{A}) (resp., (S, τ_{S})) if and only if (A, τ_{A }∩ L_{θ}) (resp., (S, τ_{S }∩ L_{θ})) is a topological S-act (a topological semigroup). Also, we prove that when Y is closed, the study of Rees congruence ρ_{Y }is related to the study of the lattice of open sets which contain Y.]]>Berglund, J.F. and K.H. Hofmann,1967Berglund, J.F., D.J. Hugo and M. Paul,1989Burris, S. and H.P. Sankappanavar,1981Dikranjan, D. and W. Tholen,1995Ebrahimi, M.M. and M. Mahmoudi,2001Gonzalez, G.,2001Gutik, O.V. and K.P. Pavlyk,20060-extensions of semigroups with zero.]]>Hryniv, O.,2005Khosravi, B.,2009Kilp, M., U. Knauer and A.V. Mikhalev,2000Lawson, J. and A. Lisan,1994Lawson, J.D. and B. Madison,1971Normak, P.,1993Normak, P.,2006Wolfgang, R.,1984Wallce, A.D.,1955