【作者】 徐晓泉； 刘应明；

【Author】 XU Xiao-qun~(1,2), LIU Ying-ming~1 (1. Institure of Mathematics, Sichuan University, Chengdu 610064, China; 2. Department of Mathematics, Jiangxi Normal University, Nanchang 330027,China)

【机构】 四川大学数学研究所；

【摘要】 主要讨论完备格的关系表示问题,分别建立了完全分配格的正则表示定理、超连续格的有限正则表示定理、λ-超连续格的κ-正则关系表示定理、区间拓扑T₂完备格的广义有阴正则表示定理,给出了正则关系、完全分配格、超连续格、λ-超连续格、区间拓扑T₂完备格的内蕴式刻划;给出了本文所建立的完备格的关系表示理论在Domain理论、格论和拓扑学中的若干应用。更多还原

【Abstract】 this paper is mainly devoted to the relational representations of completely distributive lattices, hypercontinuous lattices,λ-hypercontinuous lattices and complete lattices with T₂ interval topology. The regular representation of completely distributive lattices, the finitely regular representation of hypercontinuous lattices,the λ-regular representation of λ-hypercontinuous lattices and the generalized finitely regular repreentation of the complete lattices with T₂ interval topology are given. The intrinsic characterizations of regular relations, completely distributive lattices, hypercontinuous lattices,λ-hypercontinuonus lattices and the complete lattices with T₂ interval topology are obtained. Some applications of the relational repersentation theory of completer lattices in Domain theory,lattice theory and topology are given.更多还原