模糊度量空间的强嵌入  

Strong Embeddability for Fuzzy Metric Spaces

作　　者：李国强 余淑辉 LI Guoqiang;YU Shuhui(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China;School of Big Data Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China)

机构地区：[1]贵州财经大学数统学院,贵阳550025 [2]贵州财经大学大数据统计学院,贵阳550025

出　　处：《数学年刊（A辑）》2022年第4期399-414,共16页Chinese Annals of Mathematics

基　　金：2023年度贵州省教育厅高校科学研究项目(青年项目)(No.黔教技[2022]172);2022年度贵州财经大学校级项目(No.2022KYQN12)的资助。

摘　　要：本文定义了George和Veeramani意义下的模糊度量空间的强嵌入,证明了可强嵌入的模糊度量空间能够粗嵌入到Hilbert空间.另外还证明了强嵌入在模糊度量空间的粗范畴下是不变的,并给出了模糊度量空间强嵌入的一些等价刻画.In this paper,the authors define strong embeddability of fuzzy metric spaces in the sense of George and Veeramani,and prove that fuzzy metric spaces with strong embeddability are coarsely embeddable into Hilbert space.The authors also show that strong embeddability is an invariant in the coarse category of fuzzy metric spaces.Furthermore,the authors provide equivalent characterizations of strong embeddability for fuzzy metric spaces.

关 键 词：粗几何 模糊度量空间 强嵌入 粗拓扑 

分 类 号：O177.99[理学—数学]