We introduce omega-weakly-(g(1) g(2))-continuous functions on generalized topological spaces and study their relations with other classes of generalized continuous functions given in [1 8]. Then we define the notion of omega open set on generalized neighbourhood systems as omega-phi-open set. By using these sets we generate generalized topology. Also we introduce two kinds of continuity on generalized neighbourhood systems and investigate relationships between these two kinds (phiphi)-continuity and weakly-(phiphi')-continuity.
