摘要
本文利用一致覆盖的概念,讨论了度量空间的序列覆盖紧映象的结构.主要结果有: (1)空间X是局部可分度量空间的序列覆盖紧映象当且仅当X具有由cosmic子空间构成的一致sn网; (2)空间X是局部可分度量空间的序列覆盖,商紧映象当且仅当X是度量空间的序列覆盖,商紧映象且是局部cosmic空间.
In this paper the structures of sequence-covering compact images of locally separable metric spaces are investigated by uniform covers, the main results are that (1) a space is a sequence-covering compact image of a locally separable metric space if and only if it has a uniform sn-network consisting of cosmic subspaces; (2) a space is a sequence-covering quotient compact image of a locally separable metric space if and only if it is a locally cosmic space and a sequence-covering quotient compact image of a metric space.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2004年第6期1149-1154,共6页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金(10271026)
江苏省教育厅自然科学基金(02KJB110001)
福建省自然科学基金(F0310010)
关键词
序列覆盖映射
一致覆盖
点星网
Sequence-covering mappings
Uniform covers
Point-star networks
