| Ponomarev-系中的紧覆盖映射 |
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| 引用本文： | 葛英.Ponomarev-系中的紧覆盖映射[J].数学进展,2007,36(4):447-452. |
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| 作者姓名： | 葛英 |
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| 作者单位： | 苏州大学数学科学学院,苏州,江苏,215006 |
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| 摘 要： | 本文讨论了Ponomarev-系中的紧覆盖映射与集族之间的关系,得到如下结果.(1)对于Ponomarev-系(f,M,x,{P_n}),f是紧覆盖映射当且仅当每一P_n具有CFP-性.(2)对于Ponomarev-系(f,M,X,P),f是紧覆盖映射当且仅当P是X的强k-网.作为这些结果的一些应用,本文分别给出了度量空间紧覆盖π-象和度量空间紧覆盖象的内部结构.
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| 关 键 词： | 紧覆盖映射 π-映射 Ponomarev-系 σ-强网 点星网 CFP-性 强k-网 cfp-网 π-mapping σ-strong network |
| 文章编号： | 1000-0917（2007）04-0447-06 |
| 修稿时间： | 2005-04-28 |
Compact-covering Mappings in Ponomarev-systems |
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| GE Ying.Compact-covering Mappings in Ponomarev-systems[J].Advances in Mathematics,2007,36(4):447-452. |
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| Authors: | GE Ying |
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| Institution: | Department of Mathematics, Suzhou University, Suzhou, Jiangsu, 215006, P. R. China |
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| Abstract: | In this paper the relations of compact-covering mappings and some families of subsets are investigated in Ponomarev-systems, and the following results are obtained. (1) f is a compactcovering mapping if and only if every Pn has a CFP-property for a Ponomarev-system (f, M, X, {Pn}).(2) f is a compact-covering mapping if and only if P is a strong k-network of X for a Ponomarevsystem (f, M, X, P). As applications of these results, some internal structures of compact-covering,π-images of metric spaces and compact-covering images of metric spaces are obtained respectively. |
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| Keywords: | compact-covering mapping Ponomarev-system strong k-network point-star network CFP-property cfp-network |
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