关于R.M.Stephenson.Jr.定理的一个注记

A NOTE ON A THEOREM PROPOSED BY R.M.STEPHENSON.JR.

在文献[1]中,R.M.Stepheson.Jr.提出问题:是否每一个局部弱紧的,第一可数的正则的空间都存在一个第一可数的正则的一闭扩充?在此文中,我们给出了一个非弱紧而局部弱紧空间 X 具有形状为 X ∪{∞}的,第一可数的正则一闭扩充的充分必要条件,同时得到了两个有趣的推论。

In this paper we give a sufficient and necessary condition under which alocally feebly compact,first countable regular space X has a first coun tableregular—closed extension space X∩{∞}.We also get two intereting corolla-ries to above theorem.These partially answer a problem proposed by R.M.Stephenson.Jr.