模糊度量空间的强嵌入

Strong Embeddability for Fuzzy Metric Spaces

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.