报告题目：Upper powerdomain of quasicontinuous domains

报告人：吕振超教授（四川大学）

报告时间：2025年12月11日 19：00-20：00

报告地点：5278论坛 301会议室

摘要：The upper powerdomain of an arbitrary dcpo L can be constructed by the Scott completion of the directed upper powerspace of L. By means of this result, we investigate the upper powerdomains of quasicontinuous domains. The main results are: (1) The upper powerdomain P_U(L) of a quasicontinuous domain L is quasicontinuous iff the directed upper powerspace of L is endowed with the Scott topology, iff P_U(L) is isomorphic to Q(L), the semilattice of nonempty Scott compact saturated subsets of L. (2) There exists a quasicontinuous dcpo whose upper powerdomain is not quasicontinuous. (3) The upper powerdomain of a strongly quasicontinuous domain L is isomorphic to Q(L).

个人简介：吕振超，现任四川大学数学学院副教授，主要研究序拓扑理论相关的问题。2018年博士毕业于四川大学数学学院，2018-2019年于法国巴黎萨克雷高等师范学校（ENS Paris-Saclay）从事博士后研究。主持国家自然科学基金两项，已在Topology and its applications, Theoretical computer science, Mathematical structures in computer science等期刊发表多篇论文。