摘要
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.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
1999年第5期827-832,共6页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金
关键词
紧覆盖映射
ss映射
局部可数网
度量空间
Compact-covering mappings, Sequence-covering mappings, Strong s-mappings, k-networks, cs-networks, Compact-finite-partition networks