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关于局部可数网与ss映射
引用本文:李进金,江守礼.关于局部可数网与ss映射[J].数学学报,1999,42(5):827-832.
作者姓名:李进金  江守礼
作者单位:1. 漳州师范学院数学系,漳州,363000
2. 山东大学数学院,济南,250100
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.

关 键 词:紧覆盖映射  序列覆盖映射  ss映射  k网  cs网  紧有限分解网
修稿时间::1998-07-0

On Locally Countable Networks and Strong s-Mappings
Li Jinjin,Jiang Shouli.On Locally Countable Networks and Strong s-Mappings[J].Acta Mathematica Sinica,1999,42(5):827-832.
Authors:Li Jinjin  Jiang Shouli
Institution:Li Jinjin (Department of Mathematics, Zhangzhou Teacher's College, Zhangzhou 363000, P. R. China)Jiang Shouli (Department of Mathematics, Shandong University, Jinan 250100, P. R. China)(E-mail: jiang@math. sdu. edu. cn)
Abstract: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.
Keywords:Compact-covering mappings  Sequence-covering mappings  Strong s-mappings  k-networks  cs-networks  Compact-finite-partition networks
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