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.