Ponomarev-系中的紧覆盖映射(英文)  

Compact-covering Mappings in Ponomarev-systems

作　　者：葛英[1] 

机构地区：[1]苏州大学数学科学学院,苏州江苏215006

出　　处：《数学进展》2007年第4期447-452,共6页Advances in Mathematics（China）

基　　金：The work is supported by NSFC(No.1057115102,No.10671173).

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.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.

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 

分 类 号：O189.11[理学—数学]