积拓扑与箱拓扑的比较

The comparison of product topology with box topology in Cartesian product

积拓扑与箱拓扑是在拓扑空间族的笛卡儿积上引进的2种不同的拓扑,它们都是有限积拓扑的推广,对这2种拓扑作以比较是有益的。系统地讨论了积拓扑与箱拓扑的概念、性质,并对它们之间的差异作了比较。

Product topology and box topology are two methods for introducing topologies in general Cartesian product,both of them are generalization of the concept of finite product topology. It is useful to make a comparison between product topology and box topology. The concepts and some properties of product topology and box topology are investigated. On the other hand, the distinction between product topology and box topology are discussed.