局部可数弱基空间的性质(英文)

A Note on Spaces with Locally Countable Weak-bases

研究了局部可数弱基空间与局部可分度量空间之间的关系,论证了具有局部可数弱基的空间是g-可度量空间,1-序列覆盖ss-映射仍具有局部可数弱基的性质.

In this paper, firstly we establish the relationships between spaces with a locally countable weak-base and locally separable metric spaces by means of compact-covering maps, secondly we show that a regular space with a locally countable weak-base is g -metrizable. Thirdly, we show that 1-sequence-covering, quotient, ss-maps preserve spaces with a locally countable weak base.