The relations among the notions of various kinds of stability and their applications
发布时间：2024-10-25
点击次数：
影响因子：1.1
DOI码：10.1007/s43037-024-00354-w
发表刊物：Banach J. Math. Anal.
摘要：First, we prove that a random metric space can be isometrically embedded into a complete random normed module, as an application it is easy to see that the notion of d-σ-stability in a random metric space can be regarded as a special case of the notion of σ-stability in a random normed module; as another application we give the final version of the characterization for a d-σ-stable random metric space to be stably compact. Second, we prove that an Lp-normed L∞-module is exactly generated by a complete random normed module so that the gluing property of an Lp-normed L∞- module can be derived from the σ-stability of the generating random normed module, as applications the direct relation between module duals and random conjugate spaces are given. Third, we prove that a random normed space is order complete iff it is (ε, λ)-complete, as an application it is proved that the d-decomposability of an order complete random normed space is exactly its d-σ-stability. Finally, we prove that an equivalence relation on the product space of a nonempty set X and a complete Boolean algebra B is regular iff it can be induced by a B-valued Boolean metric on X,as an application it is proved that a nonempty subset of a Boolean set (X, d) is universally complete iff it is a B-stable set defined by a regular equivalence relation.
合写作者：Xiaohuan Mu, Qiang Tu
第一作者：Tiexin Guo
论文类型：期刊论文
论文编号：42
学科门类：理学
一级学科：数学
文献类型：J
卷号：18
是否译文：否
发表时间：2024-05-24
收录刊物：SCI