主讲人：李庆国 教授

报告题目：Posets uniquely determined by its Scott compact saturated subsets

报告时间：2024年12月6日下午17：00-18：00

报告地点：数学科学学院305会议室

报告摘要：Inspired by Zhao and Xu’s study on which a dcpo can be determined by its Scott closed subsets lattice, we further investigate whether a poset (or dcpo) P is able to be determined by the family Q(P) of its Scott compact saturated subsets, in the sense that the isomorphism between (Q(P),⊇) and (Q(M),⊇) implies the isomorphism between P and M for any poset (or dcpo) M, in such case, P is called Q_σ-unique. Quasicontinuous domains are proved to be Q_σ-unique posets and draw support from which, we provide a class of Q_σ-unique dcpos. We also define a new kind of posets called K_D and show that every co-sober K_D poset is Q_σ-unique. It even yields another kind of Q_σ-unique dcpos. It is gratifying that weakly well-filtered co-sober posets are also Q_σ-unique. At last, we distinguish among the conditions which make a poset (or dcpo) Q_σ-unique from each other by some examples; meanwhile, it is confirmed that none of them except the property of being co-sober are necessary for a poset (or dcpo).

个人简介：李庆国，男，汉族，生于1963年6月。博士，湖南大学数学学院二级教授，博士生导师，校学术委员会委员。1999年7月至2000年6月及2008年11月至2009年11月分别在美国科罗拉多大学数学系和康涅底克大学数学系作访问教授。2000年12月起担任湖南大学应用数学专业博士生导师。现为中国系统工程学会模糊数学与模糊系统委员会副理事长，湖南省数学学会副理事长。入选湖南省121人才第一层次，国务院政府特殊津贴获得者，湖南大学岳麓学者。曾获2013年湖南省自然科学一等奖，排名第一。已完成国家自然科学基金面上项目五项。现正承担国家自然科学基金重点项目一项。目前主要研究领域为Domain理论，非Hausdorff拓扑。至今为止，已在《Applied Categorical Structures》，《Information and Computation》，《Annals of Pure and Applied Logic》，《Information Sciences》，《Theoretical Computer Science》，《Topology and its Applications》，《Journal of Pure and Applied Algebra 》，《Fuzzy Sets and System》等国际期刊上发表论文100 余篇。