摘要
本文证明了如下结果：⑴Ｔ空间Ｘ具有σ－局部可数ｃｓ＾＊－网当且仅当Ｘ是某一度量空间的序列复盖ｍｓｓｓ－映象；⑵Ｔ＾３空间Ｘ具有σ－局部可数ｃｓ－网当且仅当Ｘ是某一度量空间的强序列复盖ｍｓｓｓ－映象。
In this paper we prove the following results: (1) A T_3 topological space X is the sequence-covering msss-image of a metric space if and only if it has a σ-locally countable cs~*-network; (2) A T_3 topological space X is the strong sequence-covering msss-image of a matric space if and only if it has a σ-locally countable cs-network.
基金
河南省自然科学基金!984062200
河南省教委科研基金!97110012
关键词
σ-局部可数族
cs-网络
度量空间
msss-映射
σ-locally countable collection
cs~*-network
cs-network: sequence-covering mapping
strong sequence-covering mapping
msss-mapping.
