Mathematical Logic Quarterly 54 (5):545-560 (2008)

Abstract
The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskiĭ, Tseĭtin, Kreisel, and Lacombe have asserted the existence of non-empty co-r. e. closed sets devoid of computable points: sets which are even “large” in the sense of positive Lebesgue measure.This leads us to investigate for various classes of computable real subsets whether they always contain a computable point
Keywords Co‐r. e. closed sets  connected component  non‐uniform computability
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DOI 10.1002/malq.200610058
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Effective Borel Measurability and Reducibility of Functions.Vasco Brattka - 2005 - Mathematical Logic Quarterly 51 (1):19-44.
The Arithmetical Hierarchy of Real Numbers.Xizhong Zheng & Klaus Weihrauch - 2001 - Mathematical Logic Quarterly 47 (1):51-66.
Computable Operators on Regular Sets.Martin Ziegler - 2004 - Mathematical Logic Quarterly 50 (45):392-404.

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