Quantitative Continuous Domains
Quantitative Continuous Domains
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定量连续域
DOI：
10.1023/a:1023012924892
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发表时间：
2003
影响因子：
0.6
通讯作者：
P. Waszkiewicz
中科院分区：
文献类型：
--
作者：
P. Waszkiewicz
我们将两种方法联系到定量域理论，Steve马修斯的部分度量和Keye Martin的测量，通过证明稳定的部分度量与弱模测量一一对应。它表明，每一个ω-代数域承认一个部分度量，其相关的测量精确地分配零的最大元素的集合，一个条件的特点突出在马丁的工作。部分度量以标准的方式产生度量;我们研究了所得空间完备的条件，并证明了每个ω-代数域都允许这种部分度量。我们讨论了一些例子和反例，以更准确地定位我们的结果的强度。
We relate two approaches to Quantitative Domain Theory, thepartial metricsof Steve Matthews and themeasurementsof Keye Martin, by showing thatstablepartial metrics are in one-to-one correspondence toweakly modularmeasurements. It is shown that every ω-algebraic domain admits a partial metric whose associated measurement assigns zero precisely to the set of maximal elements, a condition which features prominently in Martin's work. A partial metric gives rise to a metric in a standard way; we study the conditions under which the resulting space is complete and show that every ω-algebraic domain admits a partial metric of this kind. We discuss a number of examples and counterexamples to locate the strength of our results more exactly.