In this paper, we establish the necessary and sufficient condition for an equivalence relation ρ on S-act A endowed with a topology such that A/ρ becomes Hausdorff topological S-act. Also, show if A1 A2 be two S-acts, then any homomorphism ϕ : → A2, A1/ ker is only ϕ-saturated continuous. Moreover, congruences θ1 θ2 topology, ∩ congruence mapping A/θ1 × A/θ2, defined by ϕ(a) = (aθ1, aθ2), all ∈...