Topological structure of generalized rough sets

In this paper, we investigate some properties of (X,τθ)(X,τθ) such as compactness, separate property, Lindelöf   property and connectedness, where (X,τθ)(X,τθ) is induced by a reflexive relation θθ on XX which may be infinite. Moreover, we introduce the concept of approximating spaces and research their characterizations and properties. Particularly, we obtain a sufficient and necessary condition that topological spaces are approximating spaces. These will be not only conducive to better understanding basic concepts and properties of a rough set, but also have theory and actual significance to topology.