| 交C-连续偏序集 |
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| 引用本文： | 毛徐新,徐罗山.交C-连续偏序集[J].高校应用数学学报(A辑),2017,32(1). |
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| 作者姓名： | 毛徐新 徐罗山 |
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| 作者单位： | 1. 南京航空航天大学理学院,江苏南京,210016;2. 扬州大学数学科学学院,江苏扬州,225002 |
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| 基金项目： | 国家自然科学基金，江苏省高校自然科学基金，江苏高校品牌专业建设工程 |
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| 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.
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| 关 键 词： | ScottC-集 交C-连续偏序集 C-连续偏序集 分配格 |
Meet C-continuous posets |
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| MAO Xu-xin,XU Luo-shan.Meet C-continuous posets[J].Applied Mathematics A Journal of Chinese Universities,2017,32(1). |
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| Authors: | MAO Xu-xin XU Luo-shan |
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| Abstract: | The concept of meet C-continuity for posets is introduced. Properties and charac-terizations of meet C-continuity, as well as relationships of meet C-continuity with C-continuity and QC-continuity are given. Main results are: (1) A lattice which is also meet C-continuous must be distributive; (2) A bounded complete poset (bc-poset, for short) L is meet C-continuous iff ?x ∈ L and every none-empty Scott closed set S for which ∨S exists, one has x∧∨S = ∨{x∧s : s ∈ S};(3) A complete lattice is a complete Heyting algebra iff it is meet continuous and meet C-continuous;(4) A bounded complete poset is C-continuous iff it is meet C-continuous and QC-continuous; (5) Some counterexamples are constructed to show that a distributive complete lattice needn't be a meet C-continuous lattice and a meet C-continuous lattice needn't be a meet continuous lattice. |
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| Keywords: | Scott C-set meet C-continuous poset C-continuous poset distributive lattice |
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