既开又闭的集合

Discussion on the Sets both Open and Close

“在R中，除了空集和全空间以外，再没有既开又闭的集合”这一结论推广到一股的线性赋范空间（S，||·||）中，并证明出一个度量空间不存在既开又闭的集合的充要条件．

This wticle spreads the conclusion that there is no set both open and closeexcept nul set and universal set in R to the general normal linear space,and aiso gives the ample and necessary conditions aboot tha there existsno set both open and close in a metric space.