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.
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.
出处
《数学进展》
CSCD
北大核心
2011年第2期209-214,共6页
Advances in Mathematics(China)
基金
This project is supported by NSFC(No.10971185).