可度量的局部凸空间的弱集性

W-Compactness Metrizable Locally Convex Spaces

本文用非标准方法证明并推广了Ｅｂｅｒｌｅｉｎ－Ｓｍｕｌｉａｎ定理，证明了可度量的局部凸空间中Ｗ－紧，Ｗ－序列紧及Ｗ－可数紧等价。

Using the method of nonstandard analysis,we prove and generalize the theorem of Eberlein-Smulian,and obtain the equivalence of W-compact、W-coutably compact and W-sequentially compact in metrizable locally convex spaces.