In this paper we define ?-independent (a weak-version of independence), Kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and Sidon sets. These sets have the lacunarity or thinness property and are very useful indeed. For example Varopoulos used the Kronecker sets to prove the Malliavin theorem. In t...

‎In this paper first we define the morphism between geometric spaces in two different types‎. ‎We construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎The relation between hypergroups and geometric spaces is studied‎. ‎By constructing the category $qh$ of $H_{v}$-groups we answer the question...

The combination of two elements in a group structure is an element, while, hypergroup, the non-empty set. use hypergroups appears mainly certain subclasses. For instance, polygroups, which are special subcategory hypergroups, used many branches mathematics and basic sciences. On other hand, multi-fuzzy set, element universal set may occur more than once with possibly same or different membershi...

In this paper, we introduce and study the notion of a partial n-hypergroupoid, associated with a binary relation. Some important results concerning Rosenberg partial hypergroupoids, induced by relations, are generalized to the case of n-hypergroupoids. Then, n-hypergroups associated with union, intersection, products of relations and also mutually associative n-hypergroupoids are analyzed. Fina...

We study closure properties with respect to products for hypergroupoids, semihypergroups and hypergroups associated to binary relations. Using some basic category theory tools, from a certain point, the investigation turns into studying closure properties with respect to direct products for some classes of monounary multialgebras.