可膨胀空间类的逆极限与Tychonoff积  

ON INVERSE LIMITS AND TYCHONOFF PRODUCTS OF EXPANDABLE CLASS

作　　者：朱培勇[1] 蒋继光[2] 

机构地区：[1]电子科技大学应用数学学院 [2]四川大学应用数学学院,成都610064

出　　处：《数学年刊（A辑）》2004年第5期621-626,共6页Chinese Annals of Mathematics

基　　金：四川省教育厅自然科学基金(99LA48)资助的项目.

摘　　要：设P表示可膨胀、σ-可膨胀、离散可膨胀、σ-离散可膨胀这四种性质之一.本文主要证明:(1)设X=lim{Xα,παβ,∧}并且每个投射πα是开满映射,如果X是|∧|-仿紧(遗传|∧|-仿紧)的,并且每个Xα都具有性质P(遗传性质P),则X具有性质P(遗传性质P);(2)如果X=multiply from σ∈∑ Xσ是|∑|-仿紧(遗传|∑|-仿紧)空间,则具有性质P(遗传性质p)当且仅当(?)F∈[∑]<ω,multiply from σ∈∑ Xσ具有性质P(遗传性质P).The paper mainly proves the following: (1) LetX = lim{Xα, παβ, ∧} and let the projection πα be an open and onto map for each α∈∧, if X is |∧|-paracompact (resp. hereditarily |∧|-paracompact) and each Xα has property P (resp. hereditarily property P), then X has also property P (resp. hereditarily property P). (2) Let X = multiply from σ∈∑ Xσ be |∑|-paracompact (resp. hereditarily |∑|-paracompact), X has property P (resp. hereditarily property P) iff multiply from σ∈F Xσ has property P (resp. hereditarily property P) for each F∈ [∑]<ω, where P de-notes one of four properties: expanability, σ-expandability, discrete expandability, σ-discrete expandability.

关 键 词：可膨胀 σ-可膨胀 离散可膨胀 σ-离散可膨胀 |∑|-仿紧 遗传 性质p 

分 类 号：O189.11[理学—数学]