Domain Representability of Metric Spaces
Domain Representability of Metric Spaces
复制标题
度量空间的域可表示性
DOI：
10.1016/s0168-0072(96)00017-6
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
J. Blanck
中科院分区：
文献类型：
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作者：
J. Blanck
我们证明了度量空间和度量空间之间的连续函数是可用Scott-Ershev域范畴表示的域。因此，度量空间的有效性的概念继承自有效域理论。证明了具有有效度量的可分度量空间可以用有效域来表示。对于一类空间，包括欧几里德空间，得到了通常的有效性概念。Banach不动点定理是区域的最小不动点定理的一个推论。引入了半有效域的概念，并用它给出了Ceitin定理的一个新证明。
We show that metric spaces and continuous functions between them are domain representable using the category of Scott-Ershov domains. A notion of effectivity for metric spaces is thereby inherited from effective domain theory. It is shown that a separable metric space with an effective metric can be represented by an effective domain. For a class of spaces, including the Euclidean spaces, the usual notions of effectivity are obtained. The Banach fixed point theorem is a consequence of the least fixed point theorem for domains. A notion of semieffective domains is introduced and used to give a new proof of Ceitin's theorem.