拓扑空间构建思想的认知

Perceiving Topology's conceive thought

拓扑空间是集合高度抽象化的概括性产物,深入认知它的构建思想内涵是非常有必要的.文章从中英文含义诠释拓扑的直观意义,通过联系对比向量定义及Rieman积分与Lebesgue积分理论的构建思想去剖析开集定义及拓扑空间的构建思想,提出一种所谓"若即若离"的认知理念,指出了拓扑学的归属范畴及其广泛的应用前景,以及学习拓扑所带来的高品质的数学素养.

Topology is an outcome with more abstract and recapitulative property. It is very necessarilly for penetrating to cognize topology＇ s conceive thought. This paper annotations the intuitionistic meaning toward from the Chinese-English meaning of Topology, and anatomizes the definition of open set and Topology＇s conceive thought by contacting and contrasting vector definition and the conceive thought from Rieman integral calculus and Lebesgue integral calculus theories, and puts forward a kind of cognition principle socalled ＂keep sb. or sth. at an arm＇s length＂, and points out which category Topology belongs to and Topology＇s extensive applications foreground. Topology could bring high-quality mathematics makings to the learners.