Topology Group Of Ultra-topological Group

With the study of Fuzzy mathematics, the importance of Set value mapping has been highlighted. Then the upgrade of all kings of the structures, such as ordered, topological, measurable structure and algebraic structure, etc, has been brought about. Paper [1] considered the upgrade of algebraic structure, and the concept of FIX group was raised firstly. Paper [2] [3) not only defined the concept of normal FIX group and uniform HX group, but also studied the structures of all kinds of HX group systematic. The properties, structures, classifications, homomorphism and isomorphism of all kinds of FIX group have been studies respective in [4]9]. In the paper [101 two kinds of mathematical structures of topological group is upgraded, and the concept of hyper opological group is raised, and some breakthrough is done for the upgrade of topological group. On the basis of paper [l0][l1), this paper gives some further description for FIyper opological group, proved the uniform and regular properties of the fIX group of topological group, defined the subgroup, normal subgroup, quotient group of the HX group of topological group, and in the meantime, studied some properties of theirs. Finally it homemorphism, homomorphism, isomorphism and connectivity will be considered.