计算机工程与应用2017，Vol.53Issue(4)：15-18,24,5.DOI:10.3778/j.issn.1002-8331.1607-0361
交S-超连续偏序集
Meet supercontinuous posets
摘要
Abstract
The concept of meet supercontinuity for posets is introduced. Properties and characterizations of meet superconti-nuity, 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.关键词
ScottS-集/交S-超连续偏序集/S-超连续偏序集/分配格Key words
Scott S-set/meet supercontinuous poset/supercontinuous poset/distributive lattice分类
数理科学引用本文复制引用
毛徐新,徐罗山..交S-超连续偏序集[J].计算机工程与应用,2017,53(4):15-18,24,5.基金项目
国家自然科学基金(No.11671008,No.11101212,No.61472343) （No.11671008,No.11101212,No.61472343）
江苏省高校自然科学基金(No.15KJD110006). （No.15KJD110006）
