拓朴群上的超拓扑群

【作者】 刘文军；

【导师】 张振良；

【作者基本信息】 昆明理工大学 ， 应用数学， 2001， 硕士

【摘要】 随着FUZZY数学基础的研究，突出了集值映射的重要性，于是引出了各种结构的提升问题，例如序结构、拓扑结构、可测结构以及代数结构等等。文[1]考虑了代数结构的提升问题，首次提出了HX群的概念。文[2][3]分别定义了正规幂群、一致幂群，较系统地研究了各种幂群的结构。文[4]—[9]分别研究了各种幂群的性质、结构、分类、同态和同构关系。文[10][11]将拓扑群的两个数学结构分别向幂集上提升，得到了超拓扑群，对拓扑群的提升做了突破性的工作。 本文在文[10][11]的基础上，进一步研究了超拓扑群，首先以邻域定义拓扑，继而得出了超拓扑群的定义，然后证明了超拓扑群的正则性和齐性，又定义了超拓扑群的子群、正规子群与商群，同时也研究了它们的一些基本性质，最后研究了超拓扑群的同胚、同态、同构及连通性。更多还原

【Abstract】 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.更多还原