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Our aim in this paper is to give the notion of generalized topological groupoid which is a generalization of the topological groupoid by
using the notion of generalized topology defined by Csasz ´ ar [6]. We in- ´
vestigate the basic facts in the groupoid theory in terms of generalized
topological groupoids. We present the action of a generalized topological
groupoid 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 crossed
module by generalizing the concept of crossed module defined on topological groupoids. At the last part of the study, we show how a generalized
topological crossed module can be obtained from a generalized topological groupoid and how a generalized topological groupoid can be obtained
from a generalized topological crossed module.
Mustafa Habil Gursoy. (2021) Generalized Topological Groupoids, Punjab University Journal of Mathematics, Volume-53, Issue-2.
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