Generalized Topological Groupoids

Our aim in this paper is to give the notion of generalized topological groupoid which is a generalization of the topological groupoid byusing the notion of generalized topology defined by Csasz ´ ar [6]. We in- ´vestigate the basic facts in the groupoid theory in terms of generalizedtopological groupoids. We present the action of a generalized topologicalgroupoid on a generalized topological space. We obtain some characterizations about this concept that is called the generalized topological action. Beside these, we give definition of a generalized topological crossedmodule by generalizing the concept of crossed module defined on topological groupoids. At the last part of the study, we show how a generalizedtopological crossed module can be obtained from a generalized topological groupoid and how a generalized topological groupoid can be obtainedfrom a generalized topological crossed module.