Effective Properties of Sets and Functions in Metric Spaces with Computability Structure
Effective Properties of Sets and Functions in Metric Spaces with Computability Structure
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具有可计算结构的度量空间中集合和函数的有效性质
DOI：
10.1016/s0304-3975(98)00301-6
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
Yoshiki Tsujii
中科院分区：
文献类型：
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作者：
M. Yasugi;Takakazu Mori;Yoshiki Tsujii
我们考虑一个具有可计算性结构和有效分离集的抽象度量空间。在本文中，我们还引入了一种有效的σ-紧空间。定义了这种空间上实值函数的可计算性。证明了度量空间中的一些典型命题，即Baire范畴定理、Tietze扩张定理和单位分解是有效的。并证明了可计算函数在连续函数中是稠密的。
We consider an abstract metric space with a computability structure and an effective separating set. In this article, we also introduce an effectively σ-compact space. The computability of real-valued functions on such a space is defined. It is shown that some of typical propositions in a metric space, namely Baire category theorem, Tietze's extension theorem and decomposition of unity, can be effectivized. It is also proved that computable functions are dense in continuous functions.