Research On M - Structure And R (M) - Structure

Generalized topology is a generalization of topology, it riched and developed topology. In1997, A. Csaszar first researched the gen-eralized topology, and got many topological charactizations. Then, many topologist began to study generalized topology.M-structure is a special generalized topology, A.Al-Omari and T.Noiri defined M-space and studied some properties of M-open sets. Recently, M.Navaneetha-krishnan and S.Thamaraiselvi give some interesting results on M-space. In our paper, we define.M-continuous mapping, M-compact space and M-Lindelof space, and study their proper-ties. This paper is parted into three chapters,In Chapter1, we introduce some necessary symbols and prelimi-naries which are used in this paper.In Chapter2, we give the definition of M-open sets, and study the properties of M-open sets and some mappings that defined by M-open sets. Especially, we give the definition of M-compact space and M-Lindelof space, and study their properties.In Chapter3, we give the definition of r(M)-structure, and study the properties of r(M)-structure. We also define the a(M)-structure, β(M)-structure,π(M)-structure, σ(M)-structure on M-space. Fur-thermore, we study their properties and their relations.