Yazar "Gursoy, Mustafa Habil" seçeneğine göre listele

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    Generalized crossed modules and group-groupoids
    (Tubitak Scientific & Technological Research Council Turkey, 2017) Gursoy, Mustafa Habil; Aslan, Hatice; Icen, Ilhan
    In this present work, we present the concept of a crossed module over generalized groups and we call it a generalized crossed module. We also define a generalized group-groupoid. Furthermore, we show that the category of generalized crossed modules is equivalent to that of generalized group-groupoids whose object sets are abelian generalized group.
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    Generalized ring-groupoids
    (Univ Craiova, 2017) Gursoy, Mustafa Habil
    In this work, we are going to present the concept of generalized ring-groupoid. Also, we are going to investigate some characterizations about the generalized ring-groupoids. We are going to introduce the concept of generalized subring-groupoid. So we construct the category of generalized ring-groupoids. Furthermore, we are going to discuss a new class of the generalized ring-groupoids, which we will say it M-ring-groupoid. In the end of the paper, we are going to give the product of generalized ring-groupoids.
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    Generalized Topological Groupoids
    (Univ Punjab, Dept Mathematics, 2021) Gursoy, Mustafa Habil
    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 Csaszar [6]. We investigate 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.
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    On the topological generalized crossed modules
    (Univ Craiova, 2021) Gursoy, Mustafa Habil
    In this paper, we define the topological versions of the concepts of crossed module over generalized groups, which is called generalized crossed module, and generalized group-groupoid. We construct the categories of the topological generalized crossed modules and their homomorphisms and of the topological generalized group-groupoid and homomorphisms between them. We also obtain some characterizations related to the concepts of topological generalized crossed module and topological generalized group-groupoid. Finally, at the end of the work, we prove that the category of topological generalized crossed modules is equivalent to that of topological generalized group-groupoids whose object sets are commutative topological generalized groups.