On the quotient space of a generalized action of a generalized group

In this paper by using of generalized groups and their generalized actions, we define and study the notion of $T$-spaces. Moreover, we study properties of the quotient space of a $T$-space and we present the conditions that imply to the Hausdorff property for it. Moreover, we study the maps between two $T$-spaces and we consider the notion of $T$-transitivity.