报告题目 (Title)：The relations among the notions of various kinds of stability and their applications
中文标题：各种稳定性概念之间的关系及其应用
报告人 (Speaker)：郭铁信（中南大学）
报告时间 (Time)：2024年4月3日(周三) 10:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：席东盟、李晋、张德凯、吴加勇
报告摘要：First, we prove that a random metric space can be isometrically embedded into a complete random normed module, as an application of which, it is easy to see that the notion of -stability introduced for a nonempty subset of a random metric space can be regarded as a special case of the notion of -stability introduced for a nonempty subset of a random normed module, as another application we give the final version of the characterization for a -stable random metric space to be stably compact. Second, we prove that an -module is an -normed -module iff it is generated by a complete random normed module, from which it is easily seen that the gluing property of an -normed -module can be derived from the -stability of the generating random normed module, as applications the known and new basic facts of module duals for -normed -modules can be obtained, in a simple and direct way, from the theory of random conjugate spaces of random normed modules. Third, we prove that a random normed space is order complete iff it is complete with respect to the (-topology, as an application it is proved that the -decomposability of an order complete random normed space is exactly its --stability. Finally, we prove that an equivalence relation on the product space of a nonempty set and a complete Boolean algebra is regular iff it can be induced by a -valued Boolean metric d on , as an application it is proved that a nonempty subset of a Boolean set is universally complete iff it is a -stable set defined by a regular equivalence relation.