Computer Engineering and Applications ›› 2017, Vol. 53 ›› Issue (4): 15-18.DOI: 10.3778/j.issn.1002-8331.1607-0361

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Meet supercontinuous posets

MAO Xuxin1, XU Luoshan2   

  1. 1.College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
    2.College of Mathematical Science, Yangzhou University, Yangzhou, Jiangsu 225002, China
  • Online:2017-02-15 Published:2017-05-11



  1. 1.南京航空航天大学 理学院,南京 210016
    2.扬州大学 数学科学学院,江苏 扬州 225002

Abstract: The concept of meet supercontinuity for posets is introduced. Properties and characterizations of meet supercontinuity, as well as relationships of meet supercontinuity with supercontinuity and quasi supercontinuity are given. Main results are: (1)[A] lattice which is also meet supercontinuous must be distributive; (2)[A] bounded complete poset(bc-poset, for short)[L] is meet supercontinuous iff [?x∈L] and every subset [A] for which [∨A] exists, one has [x∧∨A=∨x∧a:a∈A]; (3)[A] bounded complete poset is supercontinuous iff it is meet supercontinuous and quasi supercontinuous; (4)Some counterexamples are constructed to show that a distributive complete lattice needn’t be a meet supercontinuous lattice and a continuous lattice needn’t be a meet supercontinuous lattice.

Key words: Scott S-set, meet supercontinuous poset, supercontinuous poset, distributive lattice

摘要: 利用偏序集上的Scott S-集,引入了交S-超连续偏序集概念,探讨了交S-超连续偏序集的性质、刻画及与S-超连续偏序集、拟S-超连续偏序集等之间的关系。主要结果有:(1)交S-超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S-超连续的当且仅当对任意[x∈L]及子集[A],当[∨A]存在时有[x∧∨A=∨x∧a:a∈A];(3)有界完备偏序集S-超连续的当且仅当它是交S-超连续且拟S-超连续的;(4)获得了反例说明分配的完备格可以不是交S-超连续格,连续格也可以不是交S-超连续格。

关键词: Scott S-集, 交S-超连续偏序集, S-超连续偏序集, 分配格