模糊赋范Riesz空间上序列性质研究

打开文本图片集

中图分类号：0177 文献标识码：A 文章编号：1674-0033（2025）04-0027-06

Abstract： Through the study of the properties such as the fuzzy order continuous norm of sequences in the fuzzy normed Riesz space，the consistency of the limits of the fuzzy norm convergence and the fuzzy order convergence of sequences in the fuzzy normed Riesz space is given. The properties of the fuzzy norm convergence in the fuzzy normed Riesz space are systematically expounded. The equivalent relations among increasing sequences，upward set systems and fuzzy norm Cauchy sequences in this space are deeply discussed，and the relevant properties of the fuzzy order continuous norm are elaborated in detail.It is expercted to provide a basis for the research on the properties of fuzzy positive projections，fuzzy positive operators and positivity preservation in the fuzzy normed Riesz space.

Key words： fuzzy normed Riesz space; fuzzy Banach lattice; fuzzy normed convergence

模糊序连续范数作为模糊赋范Riesz空间理论体系的核心要素，其性质深度关联着空间的代数结构与拓扑特征。（剩余10717字）