Computable real functions of bounded variation and semi-computable real numbers

Abstract. In this paper we discuss some basic properties of computable real functions of bounded variation (CBV-functions for short). Especially, it is shown that the image set of semi-computable real numbers un-der CBV-functions is a proper subset of the class of weakly computable real numbers; Two applications of CBV-functions to semi-computable real numbers produce the whole closure of semi-computable real num-bers under total computable real functions, and the image sets of semi-computable real numbers under monotone computable functions and CBV-functions are different.