On Covering Approximation Subspaces

Let (Uʹ; Cʹ) be a subspace of a covering approximation space (U; C) and X C Uʹ. In this paper, we show that ~Cʹ(X) = C(X) PI Uʹ and Bʹ(X) C B(X) p| Uʹ. Also, C(X) = c(x)p|C(Uʹ) iff (U; C) has Property Multiplication. Furthermore, some connections between outer (resp. inner) definable subsets in (U; C) and outer (resp. inner) definable subsets in (Uʹ; Cʹ) are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.