论文标题
强烈连续的域
Strongly Continuous Domains
论文作者
论文摘要
X. Xu和D. Zhao引入的强大Scott拓扑是一种新拓扑，比上层拓扑比Scott拓扑更细，更粗糙。受到连续域和超连续域的拓扑特征的启发，我们介绍了强烈连续域的概念，并研究了强连续域的某些特性。特别是，我们给出了牢固的路线关系的定义，并通过牢固的路线关系获得了强烈连续域的表征。我们证明，强烈连续域上的强大路线关系满足插值特性，并阐明强烈连续的域与连续域之间的关系，以及强烈连续的域与超连续域之间的关系。我们讨论了强大的Scott拓扑结构和强大的Lawson拓扑的特性，这是强大的Scott拓扑结构和较低拓扑结构的普遍完善，这是一个强烈的连续领域。
Strong Scott topology introduced by X. Xu and D. Zhao is a kind of new topology which is finer than upper topology and coarser than Scott topology. Inspired by the topological characterizations of continuous domains and hypercontinuous domains, we introduce the concept of strongly continuous domains and investigate some properties of strongly continuous domains. In particular, we give the definition of strong way-below relation and obtain a characterization of strongly continuous domains via the strong way-below relation. We prove that the strong way-below relation on a strongly continuous domain satisfies the interpolation property, and clarify the relationship between strongly continuous domains and continuous domains, and the relationship between strongly continuous domains and hypercontinuous domains. We discuss the properties of strong Scott topology and strong Lawson topology, which is the common refinement of the strong Scott topology and the lower topology, on a strongly continuous domain.
