A Brief Introduction to Fibrewise Topological Spaces Theory  

作　　者：Baolin GUO Yingzhao HAN 

机构地区：[1]College of Information Engineering,Dalian University,Liaoning 116622,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2012年第5期626-630,共5页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 10971125)

摘　　要：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.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.

关 键 词：Fibrewise topology Fibrewise topological spaces Fibrewise topological mapping spaces Absolute（nbd） fibrewise retract Fibrewise category. 

分 类 号：O189.11[理学—数学] O177.3[理学—基础数学]