可计算拓扑中的Rice-Shapiro定理
The Rice-Shapiro theorem in Computable Topology
摘要：
我们提供的要求，有效的可计算拓扑空间，保证赖斯-夏皮罗定理持有这些空间的可计算元素。我们表明，这些要求的放松导致类的有效可压缩的拓扑空间的赖斯-夏皮罗定理不成立。我们提出了两个建设，有效地产生可计算的拓扑空间的特殊性质，从wn-家庭和可计算树没有可计算的无限路径。使用它们，我们提出的例子，给这个类的味道。
英文摘要：
We provide requirements on effectively enumerable topological spaces which guarantee that the Rice-Shapiro theorem holds for the computable elements of these spaces. We show that the relaxation of these requirements leads to the classes of effectively enumerable topological spaces where the Rice-Shapiro theorem does not hold. We propose two constructions that generate effectively enumerable topological spaces with particular properties from wn--families and computable trees without computable infinite paths. Using them we propose examples that give a flavor of this class.
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