Yazar "Gursoy, M. Habil" seçeneğine göre listele

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    Coverings of structured Lie groupoids
    (Hacettepe Univ, Fac Sci, 2018) Gursoy, M. Habil; Icen, Ilhan
    In this work, we present some results related to coverings of structured Lie groupoids. Firstly, we obtain a covering Lie group-groupoid and a covering morphism of Lie group-groupoids from a given Lie group-groupoid by the notion of action. Secondly, we show how the Lie group structure of a Lie group-groupoid is lifted to a covering Lie groupoid. Then, we give similar results for Lie ring-groupoid which is also a structured Lie groupoid.
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    Lie Rough Groups
    (Univ Nis, Fac Sci Math, 2018) Oguz, Gulay; Icen, Ilhan; Gursoy, M. Habil
    This paper introduces the definition of a Lie rough group as a natural development of the concepts of a smooth manifold and a rough group on an approximation space. Furthermore, the properties of Lie rough groups are discussed. It is shown that every Lie rough group is a topological rough group, and that the product of two Lie rough groups is again a Lie rough group. We define the concepts of Lie rough subgroups and Lie rough normal subgroups. Finally, our aim is to give an example by using definition of Lie rough homomorphism sets G and H.
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    A Soft Approach to Ring-Groupoids
    (E D P Sciences, 2018) Oguz, Gulay; Gursoy, M. Habil; Icen, Ilhan
    This study introduces a soft approach to the concept of ring-groupoid which is the one of the structured groupoids. Some properties and characterizations of soft ring-groupoids are established. Also, the category of soft ring-groupoids constructed by the homomorphism between two soft ring-groupoids is presented.
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    Topological ring-groupoids and liftings
    (Shiraz Univ, 2006) Ozcan, A. Fatih; Icen, I.; Gursoy, M. Habil
    We prove that the set of homotopy classes of the paths in a topological ring is a topological ring object (called topological ring-groupoid). Let p : (X) over bar -> X be a covering map and let X be a topological ring. We define a category. UTRCov(X) of coverings of X in which both X and have universal coverings, and a category UTRGdCov(pi X-1) of coverings of topological ring-groupoid pi X-1, in which X and (R) over bar (0) = (X) over bar have universal coverings, and then prove the equivalence of these categories. We also prove that the topological ring structure of a topological ring-groupoid lifts to a universal topological covering groupoid.