具有和不具有可计算点的可计算闭欧氏子集
Computable Closed Euclidean Subsets with and without Computable Points
摘要：
空集当然不包含可计算点。另一方面，由于Zaslavskii，Tseitin，Kreisel和Lacombe的令人惊讶的结果断言存在非空的co-r. e。闭集缺乏可计算点：集是'大'的意义上积极勒贝格措施。我们观察到，一定的大小实际上是必要的：每一个非空的co-r. e。不含可计算点的闭实集具有连续势。这导致我们调查的各种类别的可计算的真正的子集是否一定包含一个（不一定有效地找到）可计算的点。
英文摘要：
The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskii, Tseitin, Kreisel, and Lacombe assert the existence of NON-empty co-r.e. closed sets devoid of computable points: sets which are `large' in the sense of positive Lebesgue measure. We observe that a certain size is in fact necessary: every non-empty co-r.e. closed real set without computable points has continuum cardinality. This leads us to investigate for various classes of computable real subsets whether they necessarily contain a (not necessarily effectively findable) computable point.
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