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 交一致连续偏序集 引用本文： 毛徐新,徐罗山.交一致连续偏序集[J].数学研究及应用,2019,39(5):459-468. 作者姓名： 毛徐新  徐罗山 作者单位： 南京航空航天大学理学院, 江苏 南京 210016,扬州大学数学科学学院, 江苏 扬州 225002 基金项目： 国家自然科学基金(Grant Nos.11671008; 11101212),江苏省自然科学基金(Grant No.BK20170483),江苏高校品牌专业建设工程(Grant No.PPZY2015B109). 摘    要： In this paper, as a generalization of uniform continuous posets, the concept of meet uniform continuous posets via uniform Scott sets is introduced. Properties and characterizations of meet uniform continuous posets are presented. The main results are:(1) A uniform complete poset L is meet uniform continuous iff ↑(U ∩↓ x) is a uniform Scott set for each x ∈ L and each uniform Scott set U;(2) A uniform complete poset L is meet uniform continuous iff for each∨∨x∈ L and each uniform subset S, one has x ∧S ={x ∧ s | s ∈ S}. In particular, a complete lattice L is meet uniform continuous iff L is a complete Heyting algebra;(3) A uniform complete poset is meet uniform continuous iff every principal ideal is meet uniform continuous iff all closed intervals are meet uniform continuous iff all principal filters are meet uniform continuous;(4) A uniform complete poset L is meet uniform continuous if L1 obtained by adjoining a top element1 to L is a complete Heyting algebra;(5) Finite products and images of uniform continuous projections of meet uniform continuous posets are still meet uniform continuous. 关 键 词： 一致集    一致Scott集    完备Heyting代数    交一致连续偏序集    主理想    一致连续投射 收稿时间： 2018/9/24 0:00:00 修稿时间： 2019/5/22 0:00:00 Meet Uniform Continuous Posets Xuxin MAO and Luoshan XU.Meet Uniform Continuous Posets[J].Journal of Mathematical Research with Applications,2019,39(5):459-468. Authors: Xuxin MAO and Luoshan XU Abstract: In this paper, as a generalization of uniform continuous posets, the concept of meet uniform continuous posets via uniform Scott sets is introduced. Properties and characterizations of meet uniform continuous posets are presented. The main results are: (1) A uniform complete poset $L$ is meet uniform continuous iff $\uparrow\!(U\cap \downarrow x)$ is a uniform Scott set for each $x\in L$ and each uniform Scott set $U$; (2) A uniform complete poset $L$ is meet uniform continuous iff for each $x\in L$ and each uniform subset $S$, one has $x\wedge \bigvee S=\bigvee \{x\wedge s\mid s\in S\}$. In particular, a complete lattice $L$ is meet uniform continuous iff $L$ is a complete Heyting algebra; (3) A uniform complete poset is meet uniform continuous iff every principal ideal is meet uniform continuous iff all closed intervals are meet uniform continuous iff all principal filters are meet uniform continuous; (4) A uniform complete poset $L$ is meet uniform continuous if $L^1$ obtained by adjoining a top element 1 to $L$ is a complete Heyting algebra; (5) Finite products and images of uniform continuous projections of meet uniform continuous posets are still meet uniform continuous. Keywords: uniform set  uniform Scott set  complete Heyting algebra  meet uniform continuous poset  principal ideal  uniform continuous projection 本文献已被 CNKI 等数据库收录！ 点击此处可从《数学研究及应用》浏览原始摘要信息 点击此处可从《数学研究及应用》下载免费的PDF全文