非紧致度量空间上的持久性

Persistence on Noncompact Metric Spaces

考虑非紧致度量空间上同胚的持久性问题,利用同胚的持久性、等度连续性、强拓扑稳定性、持久跟踪性等定义,证明:等度连续且拓扑稳定的同胚是持久的;同胚有持久跟踪性当且仅当该同胚是持久的且有伪轨跟踪性;有持久跟踪性的可扩同胚是强拓扑稳定的.

We considered the persistence problem of homeomorphism on noncompact metric spaces.By using the definitions of persistence,equicontinuity,strongly topological stability,and persistent shadowing property of homeomorphisms,we prove that homeomorphisms that are equicontinuity and topologically stable are persistent,homeomorphisms have persistent shadowing properties if and only if they are persistent and have pseudoorbital shadowing properties,and an expansive homeomorphis m with persistent shadowing property is strongly topologically stable.