The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskii, Tseitin. 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 (not necessarily effectively findable) computable point. (C) WILEY-VCH Verlag GmbH Co. KGaA, Weinheim