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 ∈...

laan in (ph.d thesis, tartu. 1999) introduced the principal weak form of condition $(p)$ as condition $(pwp)$ and gave some characterization of monoids by this condition of their acts. in this paper first we introduce condition (g-pwp), a generalization of condition $(pwp)$ of acts over monoids and then will give a characterization of monoids when all right acts satisfy this condition. we also ...