Computable Functions of Bounded Variation and Semi-Computable Real Numbers
نویسندگان
چکیده
In this paper we discuss some basic properties of computable real functions which have bounded variations (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 weakly computable real number class; 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.
منابع مشابه
Burchard von Braunmühl, Computable Real Functions of Bounded Variation and Semi-computable Real Numbers
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 ...
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