In this paper,we investigate the topological stability and pseudo-orbit tracing property for homeomorphisms on uniform spaces.We introduce the concept of topological stability for homeomorphisms on compact uniform spa...In this paper,we investigate the topological stability and pseudo-orbit tracing property for homeomorphisms on uniform spaces.We introduce the concept of topological stability for homeomorphisms on compact uniform spaces and prove that if a homeomorphism on a compact uniform space is expansive and has pseudo-orbit tracing property,then it is topologically stable.Moreover,we discuss the topological stability for homeomorphisms on uniform spaces from the view of localization.We introduce definitions of topologically stable point and shadowable point for homeomorphisms on uniform spaces and show that every shadowable point of an expansive homeomorphism on a compact uniform space is topologically stable.展开更多
基金Supported by NNSF of China(Grant Nos.11861010,11761012)NSF for Distinguished Young Scholar of Guangxi Province(Grant No.2018GXNSFFA281008)+2 种基金supported by the Cultivation Plan of Thousands of Young Backbone Teachers in Higher Education Institutions of Guangxi ProvinceProgram for Innovative Team of Guangxi University of Finance and EconomicsProject of Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing(Grant No.201801ZZ03)。
文摘In this paper,we investigate the topological stability and pseudo-orbit tracing property for homeomorphisms on uniform spaces.We introduce the concept of topological stability for homeomorphisms on compact uniform spaces and prove that if a homeomorphism on a compact uniform space is expansive and has pseudo-orbit tracing property,then it is topologically stable.Moreover,we discuss the topological stability for homeomorphisms on uniform spaces from the view of localization.We introduce definitions of topologically stable point and shadowable point for homeomorphisms on uniform spaces and show that every shadowable point of an expansive homeomorphism on a compact uniform space is topologically stable.
