Discussion On The Separation In Generalized Topological Spaces

The concept of generalized topological space was introduced by A. Csasazar, a Hungarian mathematician, in 2002. The generalized topological structure is weaker than the general topological structure, so it has a wider range of applications. After nearly ten years of the development, the basic framework of generalized topological space has been established.Separation theory is one of the most important theory in generalized topological space. Several kinds of separation have been defined by different scholars. The thesis mainly further study on separation theory in generalized topological space and the main research contents are as follows:1. We study minimal m-open sets and maximal m-open sets in generalized topological spaces.We then investigate minimal separation axioms, minimal continuous maps and minimal irresolute maps with the help of minimal m-open sets.2. We introduce and study the concepts of m-normal spaces and gm-normal spaces in generalized topological spaces, establish their relationship with m-iT spaces for i =0,1,2,3,4.Then we give some properties of m-regular and m-normal spaces.3. We introduce new classes of sets calledsoù-sets,soú-sets,sogù-sets andsogú-sets in generalized topological spaces. Moreover, we obtain some of their fundamental properties. Then we investigate the characterizations of the sgm-closed sets and m-semi-12T spaces.