Burchard von Braunmühl, Computable Real Functions of Bounded Variation and Semi-computable Real Numbers

نویسندگان

  • Robert Rettinger
  • Xizhong Zheng
چکیده

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 under 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 numbers under total computable real functions, and the image sets of semicomputable real numbers under monotone computable functions and CBV-functions are different.

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تاریخ انتشار 2002