In this paper, we introduced a new type of open set in generalized topological spaces: ӼϢ-open set. A new generalization of connectedness in a generalized topological space using ӼϢ-open namely ӼϢ-connectedness is defined. Also, new generalizations of continuous functions in generalized topological space will be studied here as weakly ӼϢ- continuous, strongly ӼϢ- continuous and ӼϢ- irresolute functions.