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Öğe ACTIONS OF SOFT GROUPS(2019) Oğuz, Gülay; İçen, İlhan; Gürsoy, Mustafa HabilAbstract: The soft set theory proposed by Molodtsov is a recent mathematical approach for modeling uncertainty and vagueness. The main aim of this study is to introduce the concept of soft action by combining soft set theory with the action which is an important concept in dynamical systems theory. Moreover, di§erent types of soft action are presented and some important characterizations are given. Finally, we deÖne the concept of soft symmetric group and present the relation between the soft action and soft symmetric group, as a similar result to the classical Cayleyís Theorem.Öğe Coverings of Lie groupoids(Turkish Journal of Mathematics, 2011) İçen, İlhan; Gürsoy, M. Habil; Özcan, A. FatihAbstract: In this work we constitute the category of coverings of the Lie fundamental groupoid associated with a connected smooth manifold. We show that this category is equivalent to the category of universal coverings of a connected smooth manifold. In addition, we prove the equivalence of the category of coverings of a Lie groupoid and the category of actions of this Lie groupoid on a connected smooth manifold. Also we present two side results related to actions of Lie groupoids on the manifolds and coverings of Lie groupoids.Öğe Öğe The equivalence of 2-groupoids and crossed modules(Communications Series A1: Mathematics and Statistics, 2000) İçen, İlhanThe equivalence of 2-groupoids and crossed modulesÖğe Lie groupoids and generalized almost paracomplex manifolds(Turkish Journal of Mathematics, 2013) Şahin, Fulya; Gürsoy, Mustafa Habil; İçen, İlhanÖz: Başlık (İngilizce): Öz (İngilizce): In this paper, we show that there is a close relationship between generalized paracomplex manifolds and Lie groupoids. We obtain equivalent assertions among the integrability conditions of generalized almost paracomplex manifolds, the condition of compatibility of source and target maps of symplectic groupoids with symplectic form and generalized paraholomorphic maps.Öğe On soft topological categories(Hacettepe Journal of Mathematics and Statistics, 2019) Oğuz, Gülay; Gürsoy, M. Habil; İçen, İlhanÖz: In this paper, we introduce the notion of a soft topological category as a natural consequence of the existence of topological category and soft category. Some examples of the soft topological categories are given. The properties of soft topological category are investigated and some important results are obtained. Also, the notion of topological functor is extended to the notion of soft topological functor. Finally, we present some examples about it. Mathematics Subject Classification (2010). 18A05, 22A05, 55U40, 97H40Öğe A sheaf of R-algebras on the dual set of dual numbers(Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 1999) İçen, İlhan; Yıldız, CemilAbstract: Bu makalede, D dual sayıları üzerinde tanımlanan dual sürekli fonksiyonlar yardımıyla R-cebirlerinin ön-demeti tanımlanmış ve bu öndemete karşı gelen R-cebirlerinin demeti elde edilmiştir. Sonuç olarak herhangi U?D açık altkümesi ve R-cebirlerinin demeti için, CU=˜?(U,SD)=˜SD|DU=˜?SD|DU=˜?(U,?SD) genel sonucu elde edildi.Öğe Topological Group-Groupoids and Equivalent Categories(2022) Özcan, Abdullah Fatih; İçen, İlhanThe concept of groupoid was offered by Brandt (1926). The structure of the topological groupoid was given by Ehresmann (1958). A groupoid action is a significant appliance in algebraic topology offered by Ehresmann. Another algebraic notion is a covering given by Brown (1988). The topological group-groupoids (?-groupoid) were first put forward by Icen & Ozcan (2001). The definition of coverings of topological ? groupoid and actions of topological ?-groupoid were also presented by Icen et al. (2005). In this paper, we are going to create a category T?GpdCov(?) of covering morphisms of T?-groupoid and a category T?GpdOp(?) of actions of T?-groupoid. We will then prove that these categories are equivalent.
