机构地区: 广东海洋大学理学院
出 处: 《广东海洋大学学报》 2007年第1期64-68,共5页
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。 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 f^K 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.