关于局部可数网与ss映射

On Locally Countable Networks and Strong s-Mappings

本文建立了度量空间在几类序列覆盖ss映射下象空间的特征，讨论了局部可数集族与局部可数基（弱基）之间的相互关系，特别地证明了几类具有特定性质的局部可数网的正则空间与度量空间的几类序列覆盖ss映象之间相互等价，回答了Tanaka提出的一个问题．

In this paper, we establish the characterizations of metric spaces under strong compact-covering(compact covering, strong sequence-covering) strong s-mappings. It is shown that the regular spaces with a locally countable k-network (strong k-network,csnetwork, cs*-network, compact-finite-partition network, sequence-finite-partition network) are mutually equivalent to the images of metric spaces under strong compactcovering (compact-covering, strong sequence-covering, sequence-covering, sequencequotient) strong s-mappings. In addition, we obtain some theorems on quotient strong s-images of metric spaces.