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

时  间：2016年5月20日15:30

地  点：知新楼B1032

摘  要：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.

赵彬教授简介：1993年获四川大学博士学位，1998年破格晋升为教授。主要从事格上拓扑学与非经典数理逻辑方面的研究工作，目前正在主持国家自然科学基金重点项目。