Research On New Separation And Weak M-continuous Mapping Of M-structures

Generalized Topological is a generalization of generalized topolo-gy, which has some good properties in generalized topology, at the same time, it has enriched and developed the study of general topol-ogy. In 1997, The Hungarian mathematician A. Csaszar first defined the generalized topology, and studied the properties of generalized topological and generalized continuous. and obtained many useful results. In 2012, A.Al-Omari and T.Noiri defined the M-structure, in the same year, M.Navaneetha-krishnan and S.Thamaraiselvi further studied some properties of the M-structure. In 2015, Li Zhongyuan studied the separation properties of M-structure and the continuous mapping of (M1,M2),and got a lot of useful results. On the basis of previous scholars, we study the new separation properties of M-structure and the weak continuous mapping of M-structure. This paper is parted into three chapters.In Chapter 1. We give the definition of M-structure and intro-duce the background of M-structure, at the same time, we give the necessary symbols and preliminaries which are used in this paper.In Chapter 2. On the basis of M-space, we give the definitions of gM-closed sets, M-kernel,M-T1/2 space, and we discuss their re-lated properties, at the same time, we study some properties and relationships of the new separation in the M-R0 and M-R1 space.In Chapter 3. We give the definition of weak M-continuous map-ping and weak M-closure continuous mapping. Furthermore we s-tudy the properties of weak M-continuous mapping and the rela-tionship between weak M-continuous mapping and weak M-closure continuous mapping.