关于Frechet空间结构的一个定理

A THEOREM ON FRECHET SPACE STRUCTURE

本文讨论了Frechct空间的结构,证明了:Frechet空间X中的闭集K是紧的当且仅当存在x_n∈x,使得x_n→0(n→∞)。并且K(?){x_n}。由此可以得到推广到Frechet空间的Mazur定理的一种证明方法。

This article discusses the Frechet space structure. The result shows that closed set K in Frechet space X is compact if and only if there exist x_n∈X such that x_n→0(n→∞) and K(?){x_n}. From the result we can prove the extended Mazur's theorem in Frechet space.