| N0-sn-网的注记 |
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| 引用本文： | 王培,葛洵,刘士琴.N0-sn-网的注记[J].山东大学学报(自然科学版),2011(4):118-120. |
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| 作者姓名： | 王培 葛洵 刘士琴 |
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| 作者单位： | [1]玉林师范学院数学与计算机科学系,广西玉林537000 [2]江苏科技大学张家港校区,江苏张家港215600 [3]衡水学院数学与计算机学院,河北衡水053000 |
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| 基金项目： | 广西自然科学基金资助项目（0728035）;玉林师范学院青年基金资助项目（2009YJQN14） |
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| 摘 要： | 利用序列商映射建立了具有可数N0-sn-网的空间与可分度量空间之间的联系,讨论了可分度量空间的可数到一、序列商映像。证明了在序列空间中,下列叙述等价：（1）X有σ-离散的N0-sn-网;（2）X有σ-局部有限的N0-sn-网;（3）X有σ-遗传闭包保持的N0-sn-网;（4）X是N0-sn-弱第一可数的N-空间;（5）X有由闭子集构成的σ-紧有限的N0-sn-网。
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| 关 键 词： | N0-sn-网 N0-弱基 序列商映射 可数到一映射 |
A note on N0-sn-network |
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| WANG Pei,GE Xun,LIU Shi-qin.A note on N0-sn-network[J].Journal of Shandong University(Natural Science Edition),2011(4):118-120. |
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| Authors: | WANG Pei GE Xun LIU Shi-qin |
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| Institution: | 1. Department of Mathematics and Computer Science, Yulin Normal University, Yulin 537000, Guangxi, China; 2. Campus of Zhangjiagang, Jiangsu University of Science and Technology, Zhangjiagang 215600, Jiangsu, China; 3. Department of Mathematics and Computer, Hengshui College, Hengshui 053000, Hebei, China) |
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| Abstract: | The relations between a space with countable R0-sn-network and separable metric spaces are established by means of sequentially quotient map, and separable metric space is discussed by sequentially quotient and countable-to-one maps. The following are equivalent and proved for a sequence space X： （ 1 ） X has ao--discrete Ro-sn-network, （2） X has a o--locally finite N0-sn-network, （3） X has a tr-hereditadly closure-preserving N0-sn-network, （4） X is an Ro-sn- weakly first-countable and R-space, and （5） X has an tr-compact-finitei, N0-sn-network consisting of closed subsets. |
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| Keywords: | N0-sn-network N0-weak base sequentially quotient map countable-to-one maps |
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