Some Notes on Fine Computability
Some Notes on Fine Computability
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关于精细可计算性的一些注释
DOI：
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发表时间：
2002
期刊：
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通讯作者：
V. Brattka
中科院分区：
文献类型：
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作者：
V. Brattka
Fine定义的度量在单位区间上推导出一个严格强于普通欧氏拓扑的拓扑，它在Walsh分析中有一些有趣的应用。我们研究了实数对应的精细表示的可计算性，并构造了表征这种表示的结构。此外，我们引入了一类一般的精细可计算函数，并将其与Mori定义的局部一致精细可计算函数进行了比较。这两类函数包括所有普通的可计算函数，以及一些重要的相对于通常的欧几里得度量不连续的函数。最后证明了精细连续函数空间上的积分算子是下半可计算的。
A metric defined by Fine induces a topology on the unit interval which is strictly stronger than the ordinary Euclidean topology and which has some inter- esting applications in Walsh analysis. We investigate computability properties of a corresponding Fine representation of the real numbers and we construct a structure which characterizes this representation. Moreover, we introduce a general class of Fine computable functions and we compare this class with the class of locally uniformly Fine computable functions defined by Mori. Both classes of functions include all ordinary computable functions and, additionally, some important functions which are discontin- uous with respect to the usual Euclidean metric. Finally, we prove that the integration operator on the space of Fine continuous functions is lower semi-computable.