关于紧度量空间之间同胚映射可扩性的一个注记  

A Note on Expansive Homeomorphisms Between Compact Metrizable Spaces

作　　者：谷建胜[1] 

机构地区：[1]苏州科技学院数学系,江苏苏州215009

出　　处：《西南师范大学学报（自然科学版）》2005年第4期609-611,共3页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：江苏教育厅高校科研资助项目(00KJB110007)

摘　　要：映射:φX——>Y称为覆盖映射,如果φ是k到1的开的局部同胚映射.证明了定理“对于紧度量空间之间的同胚映射f:X——> X及g:Y ——>Y,如果存在覆盖映射:φX ——>Y,使得gφ=φf,则f可扩蕴含g可扩”中的映射φ所含条件“k到1”可以省略.The mapping φ： X→Y is a covering mapping if φ is an “k-to-1”, open, local homeomorphism. It is proved that the condition “k-to-1”, which is involved in φ in the theorem “if there is a covering mapping φ： X→Y such that φf=gφ, then f is expansive and it implies g is expansive, where f： X→X and g： Y→Y are homeomorphisms, X and Y are compact metrizable spaces”, can be omitted.

关 键 词：紧度量空间 可扩性 同胚映射 覆盖映射 

分 类 号：O189.1[理学—数学]