In this paper, we initiate the study of generalized topological groups. A generalized topological group has the algebraic structure of groups and the topological structure of a generalized topological space defined byÁ. Császár [2] and they are joined together by the requirement that multiplication and inversion are G-continuous. Every topological group is a G-topological group whereas converse is not true in general. Quotients of generalized topological groups are defined and studied. The

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... tive mapping f is called a G-homeomorphism from X to Y if both f and f −1 are G-continuous. If there is a G-homeomorphism between X and Y they are said to be G-homeomorphic denoted by X G Y. . V is called generalized neighborhood (G-neighborhood) of x ∈ X and ψ is called a generalized neighborhood system (G-neighborhood system) on X. The collection of all G-neighborhood systems on X will be denoted by Ψ(X). The following result gives the relation between G-open sets and G-neighborhood systems by combining 1.2 and 1.3 of [2] . Definition 1.4. ([2]) Let X be any set and let Ψ and G be G-neighborhood system and G-topology on X respectively. Let A ⊂ X. A point x ∈ X is called G-interior point of A if there exists a subset V ∈ ψ(x), V ⊂ A.