On Continuity of a Function Concerning Dynamics on Circle

Properties of Continuity and Dynamics on Circle

Abstract

In this paper we obtain some subsets of the set IR of real numbers on which fractional part function is continuous as a real-valued function of a real variable. Every real number can be written as the sum of its integral part and fractional part. This gives rise to fractional part function as a real-valued function of a real variable. This function is helpful in the study of dynamics on circle. Some properties of such subsets of IR are obtained.