Abstract
The regionally proximal relation and equicontinuity have the strong connection. It is well-known that a topological dynamical system is equicontinuous if and only if no distinct pair is regionally proximal. In this paper, we introduce the regionally proximal relation via Furstenberg family and show the relationship between F-equicontinuity and kF-regionally proximal relation. More preciously, if a Furstenberg family F is a filter, then a topological dynamical system is F-equicontinuous if and only if no distinct pair is kF-regionally proximal, which is a generalization of the previous result. By using this, we give a maximal F-equicontinuous factor of some topological dynamical systems and also show that F-equicontinuity and F-distality of induced system on hyperspace are equivalent.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call