【摘要】 设X和～X为度量空间,且X是紧致的,f是X上连续自映射,证明了:若fk有PWPOTP(PWPOTP+),则f有PWPOTP(PWPOTP+);满射f有PWPOTP(PWPOTP+)当且仅当由(X,f)生成的逆极限系统(Xf,σf)上转移自映射σf有PWPOTP(PWPOTP+);PWPOTP(PWPOTP+)是拓扑共轭不变性;设f,g分别为X～和X上自同胚(自映射),π∶～X→X为局部等距覆盖映射,且πf=gπ,若有δ0>0,使对x～∈～X和δ>0(δ≤δ0),x～的半径为δ的开球Uδ(x～)连通,且πUδ(x～)为等距映射,则f有PWPOTP(PWPOTP+)当且仅当g有PWPOTP(PWPOTP+);恒等映射id有PWPOTP当且仅当X是完全不连通的。更多还原

【Abstract】 Let X and X be metric spaces and X be compact, and let f be a continuous map from X to itself. In this paper, the following statements were proved: If fk has PWPOTP(PWPOTP+),then f has PWPOTP(PWPOTP+);Let f be a surjection and (Xf,df) be the inverse limit space generated by (X,f),and σf be the shift map on Xf.then f has PWPOTP(PWPOTP+)if and only if σf has PWPOTP(PWPOTP+);PWPOTP(PWPOTP+)is an invariant property under topological conjugation;Let f∶X → X and g∶X → X be homeomorphisms (continuous maps), and π∶X → X be a locally isometric covering map such that π°f=g°π.If there exists δ0>0 such that for each x∈ X and δ>0(δ≤δ0) the open ball Uδ(x) of x with radius δ is connected and π│Uδ(x) is an isometry,then f has PWPOTP(PWPOTP+)if and only if g has PWPOTP(PWPOTP+); The identity map id has PWPOTP if and only if X is totally disconnected.更多还原