On Rough Perfect Mappings

Abstract

In this paper we depend on the work of Z. Pawalak [5] who provided us with the definition and the first basic information about what so called later, the rough set theory. Here we introduce the notion of rough perfect mappings and show that such mappings can transfer some rough properties between rough topological spaces. Also, it is proved that a rough perfect map can transfer a rough compactly generated property between rough spaces instead of a rough homeomorphism, which was proved in [4]. A concept of a rough locally compact space is defined, and shown that a rough surjective continuous function between such space and a rough Hausdorff space is a rough perfect map. In addition, it is shown that a rough perfect map can preserve the rough Hausdorff property. Finally, some new rough topological properties are defined and studied with appropriate detailed proofs, which are needed throughout this work.