The transitivity of one disconnecting arc spaces

Abstract EN

Let D be a one disconnecting arc space, f: D→D be a continuous map, in this workwe get: 1- If f is transitive map.

Then the set of all periodic points is dense in D.2- If f is transitive and has a point of odd period greater than one if and only if f2is transitive and f has dense periodic points.3- f2 is transitive and f has dense periodic points if and only if f is totally transitive4- f is totally transitive if and only if f is topologically mixing.5- If f is piecewise monotone Then f is topologically mixing if and only if forevery arc K⊆D, there is an n such that f^n (K)=D.