This paper is concerned with the proper way to effectivize the notion of a Polish space. A theorem is proved that shows the recursive Polish space structure is not found in the effectively open subsets of a space \({\mathcal {X}}\), and we explore strong evidence that the effective structure is instead captured by the effectively open subsets of the product space \(\mathbb {N}\times {\mathcal {X}}\).

中文翻译：

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递归抛光空间

本文关注的是使波兰空间概念有效化的正确方法。证明了一个定理，表明在空间\({\mathcal {X}}\)的有效开子集中找不到递归波兰空间结构，我们探索了有效结构反而被有效开集捕获的有力证据乘积空间的子集\(\mathbb {N}\times {\mathcal {X}}\)。