报告题目：A kind of close connection between topology and order

报 告 人：赵彬教授，陕西师范大学

报告时间：2016年11月17日下午2:30-4:00

报告地点：A10-217

主要内容：

Let P be a partially ordered set (or poset, for short). The Birkhoff–Frink–McShane introduced the definition of order-convergence in posets . In general, order-convergence is not topological, i.e., the poset P may not be topologized so that nets order-convergence if and only if they converge with respect to the topology. One basic problem here is: for what posets is the order-convergence topological ? Although it has long been known that in every completely distributive lattice the order-convergence is topological, one still has not been able to find a satisfactory necessary and sufficient condition for order-convergence to be topological in posets. In this talk, some properties of order topology and bi-Scott topology in posets are obtained. Order-convergence and o2 -convergence of nets in posets are studied. Especially, the sufficient and necessary conditions for order-convergence and o2 -convergence of nets to be topological are given for some kind of posets.Thus we presented the close connection between topology and order.

报告人简介：

   陕西师范大学原副校长，教授,博士研究生导师，数学研究所所长。主要从事格上拓扑学与非经典数理逻辑方面的研究工作。 在《Topology and its Application》、《Archive for Mathematical Logic》、《Fuzzy sets and Systems》、《中国科学》、《科学通报》、《数学学报》等期刊发表学术论文140 余篇。先后主持完成4项国家自然科学基金项目，首届全国高等院校优秀青年教师教学与科研奖励计划项目，目前正在主持国家自然科学基金重点项目。

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2016.11.15