交C-连续偏序集

发布时间：2018-03-16 15:07

  本文选题：Scott　切入点：C-集　出处：《高校应用数学学报A辑》2017年01期 　论文类型：期刊论文

【摘要】：利用偏序集上的半拓扑结构,引入了交C-连续偏序集概念,探讨了交C-连续偏序集的性质、刻画及与C-连续偏序集、拟C-连续偏序集等之间的关系.主要结果有:(1)交C-连续的格一定是分配格;(2)有界完备偏序集(简记为bc-poset)L是交C-连续的当且仅当对任意x∈L及非空Scott闭集S,当∨S存在时有x∧∨S=∨{x∧s:s∈S};(3)完备格是完备Heyting代数当且仅当它是交连续且交C-连续的;(4)有界完备偏序集是C-连续的当且仅当它是交C-连续且拟C-连续的;(5)获得了反例说明分配的完备格可以不是交C-连续格,交C-连续格也可以不是交连续格.
[Abstract]:By using the semi-topological structure of partial ordered sets, the concept of intersecting C-continuous partial ordered sets is introduced, and the properties, characterizations and properties of intersecting C-continuous partial ordered sets are discussed. Relations between quasi C- continuous partially ordered sets and so on. The main results are: 1) the lattice of intersection C- continuous must be distributive lattice / 2) bounded complete partial ordered set (abbreviated as bc-poset)L is intersected C- continuous if and only if for any x 鈭，

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