Generalized topological spaces

Let X be a nonempty set, P(X) the power set of X and t P(X). t is called a topology on X if t satisfies the following conditions: T1) /0;X 2 t T2) If U; V 2 t, then U \V 2 t T3) G = [i2IGi 2 t, for each fGi : i 2 Ig t. Then (X; t) is called a topological space. But in [2], Cs´asz´ar introduced the notions of generalized topology and generalized topological spaces in the following way; t is called generalized topology on X if t satisfies following conditions: GT1) /0 2 t, GT1) G = [i2IGi 2 t, for each fGi : i 2 Ig t. In the case (X; t) is called generalized topological space. After this definition, in the studies most of which are made by Cs´asz´ar, relationships between generalized topology and generalized open sets, normality, continuity and varieties of continuity on generalized topologies, product of generalized topologies, separation axioms on generalized topologies and similar issues are investigated. In this study, we try to present some of the above studies related to generalized topologies in a unified manner.