| Ponomarev系与可数型的（P）映射 |
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| 引用本文： | 黄丽霞.Ponomarev系与可数型的（P）映射[J].数学研究,2008,41(3):316-320. |
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| 作者姓名： | 黄丽霞 |
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| 作者单位： | 漳州师范学院数学系,福建,漳州,363000 |
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| 摘 要： | 本文讨论了3类Ponomarev系中（P）映射与子集族的精确关系，获得了下列的结论：（1）在Ponomarev系（f，M，X，P）中f是点有限（点可数）映射当且仅当P是X的点有限（点可数）网络；（2）在Ponomarev系（f，M，X，P）中f是紧有限（紧可数）映射当且仅当P是X的紧有限（紧可数）网络；（3）在Ponomarev系（f，M，X，P）中f是局部有限（局部可数）映射当且仅当P是X的局部有限（局部可数）网络．
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| 关 键 词： | Ponomarev系 (P)映射 邻域基 |
On Ponomarev-systems and Countable (P)-mappings |
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| Huang Lixia.On Ponomarev-systems and Countable (P)-mappings[J].Journal of Mathematical Study,2008,41(3):316-320. |
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| Authors: | Huang Lixia |
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| Institution: | Huang Lixia (Dept. of Mathematic and Information Science, Zhangzhou Teachers College, Zhangzhou Fujian 363000) |
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| Abstract: | In this paper the precise relations of(P)-mappings and families of subsets of topological spaces are investigated in Ponomarev-systems,and the following results are obtained.(1) f is a point- finite(point-countable) mapping iff P is a polnt-finite network(resp.point-countable network) of X for a Ponomarev-system(f,M,X,P);(2) f is a compact-finite(compact-countable) mapping iff P is a compact-finite network(compact-countable network) of X for a Ponomarev-system(f,M,X,P);(3) f is a locally finite(locally countable) mapping iff P is a locally finite network(locally countable network) of X for a Ponomarev-system(f,M,X,P). |
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| Keywords: | Ponomarev-systems (P)-mapping neighborhood base |
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