主讲人：严从华 教授

报告题目：Convex fuzzifying bornological linear spaces and their duality

报告时间：2024年10月29日晚上20:30-22:00

报告地点：数学院301

报告摘要：The main objective of this talk is to investigate convex fuzzifying bornological linear spaces and their duality. First, we introduce the notions of convex fuzzifying bornological linear spaces and locally convex fuzzifying topological linear spaces, along with several examples. Next, we study the relationship between convex fuzzifying bornological linear spaces and locally convex fuzzifying topological linear spaces, utilizing the mapping of fuzzifying bornivorous. Subsequently, we introduce the concepts of fuzzifying bornological locally convex spaces and fuzzifying topological convex bornological linear spaces. We demonstrate that the category of fuzzifying bornological locally convex spaces can be embedded as a reflective subcategory in the category of convex fuzzifying bornological linear spaces, and the category of fuzzifying topological convex bornological linear spaces can also be embedded as a reflective subcategory in the category locally convex fuzzifying topological linear spaces. Moreover, the category of fuzzifying topological convex bornological linear spaces is topological over the category of linear spaces with respect to the expected forgetful functor. Lastly, we provide several characterizations of the fuzzifying bornological topologies.

个人简介：严从华，南京师范大学三级教授，博士生导师，南京师范大学泰州学院教务处长。主要从事模糊泛函分析、格上拓扑学相关研究。已在国内外重要杂志和国际学术会议上发表学术论文近50篇，其中，SCI收录40余篇。主持国家自然科学基金面上项目3项，参与了4项国家级、省部级课题的研究工作，曾获国家高等教育教学成果奖二等奖。中国系统工程学会模糊系统与数学专业委员会常务理事，中国数学学会数学教育分会数学教育与数学文化工作组成员，江苏省数学会理事。