Semi-closed sets and their generalizations

Let X be a topological space and A⊆X is called: (i) generalized closed set (g-closed set), if clA⊆U whenever A⊆U and U is open. (ii) semi-generalized closed set (sg-closed set), if sclA⊆U whenever A⊆U and U is semi-open.(iii) generalized semi-closed set (gs-closed set), if sclA⊆U whenever A⊆U and U is open. Moreover, the complement of a g-closed set (resp. sg-closed set, gs-closed set) in X is called g-open set (resp. sg-open set, gs-open set). In this thesis study, the properties of generalized-semi-closed functions, semi-generalized closed functions, gs-open, gs-closed, sg-open, sg-closed, gs-continuous and sg-continuous functions and their relationships with each other were investigated. Additionally, the properties of new notions like semi-generalized closure, generalized-semi-closure, generalized-semi-interior operators, gs-regular, gs-normal, sg-regular and sg-normal spaces were examined.