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高校应用数学学报
高校应用数学学报  2017, Vol. 32 Issue (1): 103-108    
    
交C-连续偏序集
毛徐新1, 徐罗山2
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
Meet C-continuous posets
MAO Xu-xin1, XU Luo-shan2
1. College of Sci., Nanjing Univ. of Aeronautics and Astronautics, Nanjing 210016, China
2. School of Math. Sci., Yangzhou Univ., Yangzhou 225002, China
 全文: PDF 
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$x\in L$及非空Scott闭集$S$, 当$\vee S$存在时有$x\wedge\vee S=\vee\{x\wedge s:s\in S\}$; (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
关键词： Scott C-集;  交C-连续偏序集;  C-连续偏序集;  分配格    
Abstract: The concept of meet C-continuity for posets is introduced. Properties and characterizations 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 $\forall x\in L$ and every none-empty Scott closed set $S$ for which $\vee S$ exists, one has $x\wedge\vee S=\vee\{x\wedge s:s\in S\}$; (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.
Key words: Scott C-set    meet C-continuous poset    C-continuous poset    distributive lattice
收稿日期: 2016-06-02 出版日期: 2018-03-18
:  0153.1  
基金资助: 国家自然科学基金(11671008; 11101212; 61472343); 江苏省高校自然科学基金(15KJD110006); 江苏高校品牌专业建设工程(PPZY2015B109)
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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, 2017, 32(1): 103-108.

MAO Xu-xin, XU Luo-shan. Meet C-continuous posets. Applied Mathematics A Journal of Chinese Universities, 2017, 32(1): 103-108.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2017/V32/I1/103

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