度量空间的弱k映象  

Weak k-mapping Images of Metric Spaces

作　　者：许子良[1] 燕鹏飞[1] 

机构地区：[1]五邑大学数学物理系,广东江门529020

出　　处：《五邑大学学报（自然科学版）》2007年第4期16-20,共5页Journal of Wuyi University(Natural Science Edition)

基　　金：国家自然科学基金(10471084)

摘　　要：给出了度量空间的弱k映射的定义，由此证明了X具有σ紧有限的CS^＋网当且仅当X是度量空间诱导序列商弱k象；X具有σ紧有限的CS网当且仅当X是度量空间诱导序列覆盖弱k象；X具有σ紧有限的序列邻域网当且仅当X是度量空间诱导1序列覆盖弱k象．In this paper, the internal characterizations of some weak k-mapping images of metric spaces are studied and it is proved that a space X is an inductive sequentially quotient weak k-image of a metric space if and only if X has σ-compact finite CS^＊-networks; X is an inductive sequence-covering, weak k-image of a metric space if and only if X has σ-compact finite CS-networks; X is an inductive 1-sequence-covering weak k-image of a metric space if and only if X has σ-compact finite sequential neighborhood-networks.

关 键 词：弱k映射 σ紧有限 序列商映射 序列覆盖映射 1序列覆盖映射 

分 类 号：O189.11[理学—数学]