Using the action of a Lie group on a HYPERGROUP, the notion of Lie HYPERGROUP is defined. It is proved that tangent space of a Lie HYPERGROUP is a HYPERGROUP and that a differentiable map between two Lie HYPERGROUP is good homomorphism if and only if its differential map is a good homomorphism. The action of a HYPERGROUP on a set is defined. Using this notion, HYPERGROUP bundle is introduced and some of its basic properties are investigated. In addition, some results on qutient HYPERGROUPs are given.

Let X be a HYPERGROUP. In this paper, we study the homomorphisms on certain subspaces of L(X)* which are weak*-weak* continuous.

There has been considerable progress in the study of HYPERGROUP algebras. In some papers, we have already studied the structure of L(X), the second dual of L(X), and related problems. Here we examine the weighted case, and among other results we generalize the above results to the weighted case.

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In this paper, the new notions of "belongingness (Îg)" and "quasi-coincidence (qd)" of a fuzzy point with a fuzzy set are introduced. By means of this new idea, the concept of (a , b)-fuzzy nary subHYPERGROUP of an nary HYPERGROUP is given, where a, b Î {Îg, qd, Îg Ù qd, Îg Ú qd} and it is shown that, in 16 kinds of (a , b)-fuzzy n-ary subHYPERGROUPs, the significant ones are the (Îg , Îg Ú qd)-fuzzy n-ary subHYPERGROUPs,and the (Îg Ù qd , Îg )-fuzzy n-ary subHYPERGROUPs.