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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 Double Actions of Groups(2019) Gürsoy, Mustafa HabilAbstract: In this work, we present the concept of double action of a group ???? on a set ???? as a new concept in literature, which opens up the way for applying rich amount of algebraic topological facts and methods in the algebraic topology. Besides of this, we give some expository examples of this new concept. We also express the definition of a double action via permutations as similar to the definition of an action on a set of groups via permutations. We investigate some characterizations about the double actions. Also we prove an adaptation of Cayley’s theorem in the case of the double action.Öğe 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 Lıe örtü grupoidleri(İnönü Üniversitesi, 2007) Gürsoy, Mustafa HabilIf M is a differentiable connected manifold then there exists an universal covering manifold M having unique differentiable structure such that the covering map p : M -> M is differentiable. This fact is also true for connected Lie groups By using this fact, it is proved that the category LGdCov(G) of coverings of connected Lie groupoids which is a generalization of connected Lie groups, and the category LGdOp(G) of actions on some M differentiable manifold are equivalent. Secondly, by introducing Lie group-groupoids the category LGGdCov(G) of coverings of some G Lie group-groupoid and the category LGGdOp(G) of actions of G on connected Lie group M are established. Further, it is shown that these categories are equivalent. Finally, it is presented by launching the notion Lie ring-groupoids, a generalization of Lie group-groupoids, that the category LRGdCov(R) of coverings of R Lie ring-groupoids and the category LRGdOp(R) of actions of R on connected Lie ring M are equivalent. KEY WORDS: Groupoid, Lie groupoid, covering groupoid, Lie group-groupoid, Lie ring-groupoid.Öğe Topolojik 2-grupoidler(İnönü Üniversitesi, 2002) Gürsoy, Mustafa HabilBu çalışmada, kategori teorideki bazı cebirsel kavramların topolojik versiyo nunu tanıttık ve İçen [16] tarafından verilen " 2-grupoidler ve grupoidler üzerinde crossed modüllerin kategorilerinin denkliği " nin topolojik versiyonunu ispatladık. Bu çalışma üç bölümden oluşmaktadır. Birinci bölümde, diğer bölümlerin daha iyi anlaşılması için kategori teorinin temel kavramları ve bunların bazı özellikleri verildi. ikinci bölümde, birinci bölümde verilen tanımların topolojik versiyonları tanım landı ve böylece ilk defa topolojik 2-grupoid tanımlandı. Son bölümde ise, çalışmama esasım oluşturan topolojik 2-grupoidler ile topolo jik crossed modüller kategorilerinin denkliği verildi. Anahtar Kelimeler: Kategori, Funktor, Doğal Transformasyon, Grupoid, 2-Grupoid, Crossed Modül.
