Slightly generalized β-continuous functions

A new class of functions, called slightly generalized -conti- nuous functions is introduced. Basic properties of slightly generalized -continuous functions are studied. The class of slightly generalized - continuous functions properly includes the class of slightly -continuous functions and generalized -continuous functions. Also, by using slightly generalized -continuous functions, some properties of domain/range of functions are characterized. slightly general- ized -continuous functions and show that the class of slightly generalized -continuous functions properly includes the class of slightly -continuous functions and generalized -continuous functions. Second we obtain some new results on g -closed sets and investigate basic properties of slightly generalized -continuous functions concerning composition and restriction. Finally, we study the behaviour of some separation axioms, related prop- erties and GO -compactness, GO -connectedness under slightly generalized -continuous functions. Relationship between generalized -continuous func- tions and GO -connected spaces are investigated. In particularly, it is shown that slightly generalized -continuous image of GO -connected spaces is connected. Throughout this paper, (X; ) and (Y; ) (or X and Y ) represents a non empty topological space on which no separation axioms are assumed, unless