具有可数弱基空间的一个新特征

A New Characterization on Spaces With a Countable weak Base

本文证明了正则空间Ｘ具有可数弱基当且仅当它是具有可数ｋ网的ｋ空间并且不含闭子空间同胚于Ｓｘ。它肯定地回答了Ｙ．Ｔａｎａｋａ在１９８３年提出的一个问题。

In this paper we prove that a space has a countable weak base if and only if it is a kspace with a countable k-netsork and contains no closed copy of S.. It affirmatively answers a problem by Y. Tanaka in 1983.