论文标题
准连续域上的普遍融合
Generalized ideal convergence on quasi-continuous domains
论文作者
论文摘要
在本文中，定向完整的Poset中引入了广义理想的INF限制和广义理想最终下限限制的概念，并研究了它们与Scott Topology和Lawson拓扑的关系。主要结果如下：（1）在定向完整的POSET上，广义理想的INF-LIMIT拓扑与Scott拓扑一致； （2）普遍的理想INF-LIMITI收敛是拓扑结构，并且仅在定向的完整posets是准连续域的情况下； （3）在准连续域中，广义理想的最终下限极限拓扑与Lawson拓扑是一致的；（4）在遇到连续定向的完整poset中，普遍的理想最终下限限制是拓扑，并且仅当定向完整的POSET是连续的。
In this paper,the concepts of generalized ideal inf-limit and generalized ideal final lower bound limit are introduced in the directed complete poset,and their relations with Scott topology and Lawson topology are studied. The main results are as follows: (1) On directed complete posets,generalized ideal inf-limit topology is consistent with Scott topology; (2) Generalized ideal inf-limiti convergence is topological if and only if directed complete posets are quasi-continuous domains; (3) In quasi-continuous domain,generalized ideal final lower bound limit topology is consistent with Lawson topology;(4) In meet continuous directed complete posets,the generalized ideal final lower bound limit convergence is topological if and only if the directed complete poset is continuous.
