On Continuity of a Function Concerning Dynamics on Circle | Original Article

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.