Computability
Complexity theory of real functions
Complexity theory of real functions
Computable analysis: an introduction
Computable analysis: an introduction
Weakly computable real numbers
Journal of Complexity
A Finite Hierarchy of the Recursively Enumerable Real Numbers
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Recursively Enumerable Reals and Chaitin Omega Numbers
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Closure Properties of Real Number Classes under Limits and Computable Operators
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
On the Effective Jordan Decomposability
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
A computability theory of real numbers
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
On the turing degrees of divergence bounded computable reals
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
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Let Csc and Cwc be classes of the semi-computable and weakly computable real numbers, respectively, which are discussed by Weihrauch and Zheng [12]. In this paper we show that both Csc and Cwc are not closed under the total computable real functions of finite length on some closed interval, although such functions map always a semi-computable real numbers to a weakly computable one. On the other hand, their closures under general total computable real functions are the same and are in fact an algebraic field. This field can also be characterized by the limits of computable sequences of rational numbers with some special converging properties.