关于稠密集的若干探讨

DISCUSSION ON THE DENSE SET

在拓扑空间中探讨了稠密集与无处稠密集这两个概念的几个等价表述形式，给出了一个集合的边界与该集合闭包的边界相等的充分条件。另外，分别在 Hilbert 空间和赋范空间中讨论了稠密集的相关性质和应用。

We first discuss the equivalent descriptions of dense set and nowhere dense set in topological space,and provide the sufficient condition for the equality between the boundary of a set and the boundary of the closure of the set.Then we discuss the properties and application of dense sets in Hilbert space and normed space, respectively.