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Asymptotic dimension of fuzzy metric spaces
Fuzzy Sets and Systems ( IF 3.9 ) Pub Date : 2021-03-24 , DOI: 10.1016/j.fss.2021.03.013 Pawel Grzegrzolka
中文翻译:
模糊度量空间的渐近维
更新日期:2021-03-24
Fuzzy Sets and Systems ( IF 3.9 ) Pub Date : 2021-03-24 , DOI: 10.1016/j.fss.2021.03.013 Pawel Grzegrzolka
In this paper, we define asymptotic dimension of fuzzy metric spaces in the sense of George and Veeramani. We prove that asymptotic dimension is an invariant in the coarse category of fuzzy metric spaces. We also show several properties of asymptotic dimension in the fuzzy setting which resemble the properties of asymptotic dimension in the metric setting. We finish with calculating asymptotic dimension of a few fuzzy metric spaces.
中文翻译:
模糊度量空间的渐近维
在本文中,我们从George和Veeramani的角度定义了模糊度量空间的渐近维。我们证明渐近维数在模糊度量空间的粗分类中是不变的。我们还显示了模糊设置中渐近维的一些属性,类似于度量设置中的渐近维的属性。我们以计算一些模糊度量空间的渐近维数结束。