纤维拓扑空间理论简介

A Brief Introduction to Fibrewise Topological Spaces Theory

中文关键词:  纤维拓扑  纤维拓扑空间  纤维映射空间  纤维绝对收缩核  纤维范畴.

英文关键词:Fibrewise topology  Fibrewise topological spaces  Fibrewise topological mapping spaces  Absolute(nbd) fibrewise retract  Fibrewise category.

中文摘要:

      纤维拓扑空间理论是近20年来在一般拓扑学、代数拓扑学和纤维空间等理论的基础上发展起来的一个新的数学分支,它与微分几何学、李群以及动力系统理论有着密切的关联,并且由于从范畴论的角度来看,它是处于较一般拓扑空间理论更高一档的范畴,所以对各种纤维拓扑空间的某些新的性质与特征的探讨将更具有重要的意义.本文阐述了纤维拓扑空间理论的产生与发展过程,介绍了关于这个研究方向的一些主要论著的基本内容和某些重要的结果.最后,综述了纤维拓扑空间理论的研究现状以及与其密切相关的一些重要课题.

英文摘要:

      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.