报告题目：(L, M)-fuzzy topological vector spaces and their related bornological structures
报告人:严从华
报告时间:2026年3月27日 9:00
报告地点：综合楼 1101 室
主办单位：数学学院、吉林省数学软计算与应用重点实验室
报告摘要：
In this paper, we investigate (L, M)-fuzzy topological vector spaces and their associated fuzzy bornological structures. First, we present necessary and sufficient conditions for the continuity of additive and multiplicative mappings in (L, M)-fuzzy topological vector spaces, thereby establishing a characterization of such spaces. Furthermore, several special constructions are introduced, including quotient (L, M)-fuzzy topological vector spaces. Second, by introducing the notion of fuzzy boundedness degree within (L, M)-fuzzy topological vector spaces, we generate (L, M)-fuzzy vector bornologies from (L, M)-fuzzy linear topologies. We also examine the relationship between topological convergence and bornological convergence, as well as the continuity and boundedness properties of linear mappings. Finally, we demonstrate that certain fundamental (L, M)-fuzzy bornologies--such as initial, product, and quotient (L, M)-fuzzy bornological structures which can be induced by corresponding (L, M)-fuzzy topologies.
报告人简介:
严从华，南京师范大学数学科学学院教授，博士生导师。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50余，其中，SCI收录近50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类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。
