In this paper we consider some fundamental properties of generalized rough sets induced by binary relations on algebras and show that 1.Any reflexive binary relation determines a topology.2.If θ is a reflexive and symmetric relation on a set X, then O={A⊆X|θ-(A)=A} is a topology such that A is open if and only if it is closed.3.Conversely, for every topological space (X,O) satisfying the condition that A is open if and only if it is closed, there exists a reflexive and symmetric relation R such that O={A⊆X|R-(A)=A}.4.Let θ be an equivalence relation on X. For any pseudo ω-closed subset A of X,θ − (A) is an ω-closed set if and only if ω(x,x,…,x)∈θ − (A) for any x∈X.Moreover we consider properties of generalized rough sets.