The Periodicity of Two Disconnecting Arc ‎Spaces

Abstract

Let  be two disconnecting arc and  be a continuous map . Suppose has a fixed point and a periodic point of period n for some odd integer .Then for every integer  ,  has a periodic point of period  . If  have periodic points of period  and  where  are odd integer numbers , then the set of periodic points are infinite . Finally , if the set of periodic points is finite , then there are two integers  and  with  and  such that the set of period is .