性质A与模糊度量空间的粗可嵌入性
Property A and coarse embeddability for fuzzy metric spaces
摘要：
性质A是一个几何性质，最初是为离散度量空间引入的，以提供可粗嵌入希尔伯特空间的充分条件，并且它是通过在精神上类似于群的顺从性的经典概念的Følner条件定义的。本文在George和Veeramani意义下定义了Fuzzy度量空间的性质A，证明了它是Fuzzy度量空间的粗范畴中的不变量，并给出了一致局部有限Fuzzy度量空间的性质A的刻画.证明了具有性质A的一致局部有限模糊度量空间可粗嵌入到希尔伯特空间中.
英文摘要：
Property A is a geometric property originally introduced for discrete metric spaces to provide a sufficient condition for coarse embeddability into Hilbert space, and it is defined via a Følner condition similar in spirit to the classical notion of amenability for groups. In this paper, we define property A for fuzzy metric spaces in the sense of George and Veeramani, show that it is an invariant in the coarse category of fuzzy metric spaces, and provide characterizations of it for uniformly locally finite fuzzy metric spaces. We also show that uniformly locally finite fuzzy metric spaces with property A are coarsely embeddable into Hilbert space.
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