Rough sets theory is an important method for dealing with uncertainty, fuzziness and
undefined objects. In this paper, we introduce a new approach for generalized rough sets based on
the neighborhood systems induced by an arbitrary binary relation. Four pairs of the dual approxima-
tion operators are generated from the core of neighborhood systems. Relationship among different
approximation operators are presented. We generate different topological spaces by using the core of
these neighborhood systems. Relationship among different generated topologies are discussed