Please wait a minute...
高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (1): 103-108    DOI:
    
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
Download:
Export: BibTeX | EndNote (RIS)      

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     
Received: 02 June 2016      Published: 18 March 2018
CLC:  0153.1  
  0189.1  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
MAO Xu-xin
XU Luo-shan
Cite this article:

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

URL:

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


交C-连续偏序集

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 
No related articles found!