Abstract

The investigation of computability in topological structures develops in some aspects similar to the investigation of computability in algebraic structures. If a countable algebraic structure is not computably presentable then its ‘‘degree of non-computability’’ is measured by the so called degree spectrum, i.e. the set of Turing degrees that compute an isomorphic copy of the structure. In this note we initiate a discussion of similar notions for topological structures, in particular we describe the degree spectra of domains.

中文翻译：

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拓扑空间的度谱

摘要

拓扑结构中可计算性的研究在某些方面与代数结构中可计算性的研究类似。如果可数代数结构不可计算地表示出来，则通过所谓的度谱（即计算结构同构副本的图灵度集）来测量其“不可计算度”。在本说明中，我们开始讨论拓扑结构的类似概念，尤其是描述域的度谱。