Fibrewise topological spaces theory, presented in the recent 20 years, is a new branch of mathematics developed on the basis of General Topology, Algebra topology and Fibrewise spaces theory. It is associated with dif...Fibrewise topological spaces theory, presented in the recent 20 years, is a new branch of mathematics developed on the basis of General Topology, Algebra topology and Fibrewise spaces theory. It is associated with differential geometry, Lie groups and dynamical systems theory. From the perspective of Category theory, it is in the higher category of general topological space, so the discussion of new properties and characteristics of the variety of fibre topological space has more important significance. This paper introduces the process of the origin and development of Fibrewise topological spaces theory. Then, we study the main contents and important results in this branch. Finally, we review the research status of Fibrewise topological spaces theory and some important topics.展开更多
In general category, the group of self-equivalences of sum object can decompose as the product of its two subgroups under certain conditions and also several split short exact sequences are obtained. Subsequently, we ...In general category, the group of self-equivalences of sum object can decompose as the product of its two subgroups under certain conditions and also several split short exact sequences are obtained. Subsequently, we apply the above results to the category of space under a space and get some results which are dual to those in fibrewise category.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 10971125)
文摘Fibrewise topological spaces theory, presented in the recent 20 years, is a new branch of mathematics developed on the basis of General Topology, Algebra topology and Fibrewise spaces theory. It is associated with differential geometry, Lie groups and dynamical systems theory. From the perspective of Category theory, it is in the higher category of general topological space, so the discussion of new properties and characteristics of the variety of fibre topological space has more important significance. This paper introduces the process of the origin and development of Fibrewise topological spaces theory. Then, we study the main contents and important results in this branch. Finally, we review the research status of Fibrewise topological spaces theory and some important topics.
文摘In general category, the group of self-equivalences of sum object can decompose as the product of its two subgroups under certain conditions and also several split short exact sequences are obtained. Subsequently, we apply the above results to the category of space under a space and get some results which are dual to those in fibrewise category.
