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 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 semi-computable real numbers under monotone computable functions and CBV-functions are different.
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Rettinger, R., Zheng, X., von Braunmühl, B. (2002). Computable Real Functions of Bounded Variation and Semi-computable Real Numbers. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_7
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DOI: https://doi.org/10.1007/3-540-45655-4_7
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