| 关于Ponomarev-系统的一些注记(英文) |
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| 引用本文： | 葛洵.关于Ponomarev-系统的一些注记(英文)[J].数学进展,2011(2). |
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| 作者姓名： | 葛洵 |
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| 作者单位： | 苏州大学数学科学学院;江苏科技大学张家港校区; |
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| 基金项目： | This project is supported by NSFC(No.10971185). |
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| 摘 要： | 本文给出一个反例,证明了在一个Ponomarev-系统(f,M,X,P)中,P是点有限不蕴涵f是紧有限.这纠正了有关Ponomarev-系统的一个错误命题.作为Ponomarev-系统(f,M,X,P)的进一步结果,本文分别给出了f是紧映射以及P是点有限的充分必要条件.此外,本文还给出了Ponomarev-系统中映射与网络的一些其他关系.
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| 关 键 词： | Ponomarev-系统 紧映射 点有限网 |
Remarks on Ponomarev-systems |
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| GE Xun.Remarks on Ponomarev-systems[J].Advances in Mathematics,2011(2). |
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| Authors: | GE Xun |
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| Institution: | GE Xun (1.School of Mathematical Science,Soochow University,Suzhou,Jiangsu,215006,P.R.China,2. Zhangjiagang Campus,Jiangsu University of Science and Technology,Zhangjiagang,215600,P.R.China) |
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| Abstract: | In this paper,it is proved that there exists a Ponomarev-system(f,M,X,P) such that P is point-finite and f is not a compact mapping,which shows that a proposition on Ponomarev-systems is not true.As further investigations of Ponomarev-system(f,M,X,P), this paper gives sufficient and necessary conditions such that f is a compact mapping and P is point-finite in Ponomarev-systems(f,M,X,P) respectively.Also,this paper establishes some relations between mappings and networks in Ponomarev-systems. |
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| Keywords: | Ponomarev-system compact mapping point-finite network |
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