Base-complexity classifications of qcb0-spaces1
Base-complexity classifications of qcb0-spaces1
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DOI：
10.3233/com-150044
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Matthew de Brecht;M. Schröder;V. Selivanov
中科院分区：
文献类型：
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作者：
Matthew de Brecht;M. Schröder;V. Selivanov
基于基的复杂性度量的思想，我们定义并研究了qcb_0-空间的新分类.新的分类补充了在[7，8]中引入的qcb\（_0\）-空间的层次所给出的分类，并提供了研究基于非可数的qcb\（_0\）-空间的新工具。作为副产品，我们证明了不存在泛qcb\（_0\）-空间，并建立了可数类型的Kleene-Kreisel连续泛函的几个明显新的性质。
We define and study new classifications of qcb\(_0\)-spaces based on the idea to measure the complexity of their bases. The new classifications complement those given by the hierarchies of qcb\(_0\)-spaces introduced in [7, 8] and provide new tools to investigate non-countably based qcb\(_0\)-spaces. As a by-product, we show that there is no universal qcb\(_0\)-space and establish several apparently new properties of the Kleene-Kreisel continuous functionals of countable types.