拓扑线性空间中的一致连续性和紧性

ON UNIFORM CONTINUITY AND COMPACTNESS IN TOPOLOGICAL LINEAR SPACES

拓扑线性空间中的点集E是紧的,当且仅当每个连续函数f:E→R都是一致连续的,且对于任何O邻域U,E\(A+U)都是有限集,其中A是E的导集。

A set K in topological linear space is compact if and only if the following hold:every continuous function (?):E→R is uniformly continuous,and for every O-neighborhood U,E\(A+U) is finite set, where A is derived set of the set K.