$$\Phi $$-Contraction principle and an open problem in GV-fuzzy metric spaces

Jain, Manish; Kumar, Sanjay; Park, Choonkil

doi:10.1007/s11784-020-00816-2

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2020

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Cited by 5 publications

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“…George and Veeramini slightly modified the definition of fuzzy metric spaces in [3] to show that every fuzzy metric space induces a Hausdorff topology. The modified version gained much popularity (see for example [6], [11], [14], [15], [18]) and is now considered to be the appropriate notion of metric fuzziness (see [7], [16]). Fuzzy metric spaces account for the uncertainty of measurements of the distance between any two points.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic dimension of fuzzy metric spaces

Grzegrzolka

2020

Preprint

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In this paper, we define asymptotic dimension of fuzzy metric spaces in the sense of George and Veeramini. We prove that asymptotic dimension is an invariant in the coarse category of fuzzy metric spaces. We also show several consequences of asymptotic dimension in the fuzzy setting which resemble the consequences of asymptotic dimension in the metric setting. We finish with calculating asymptotic dimension of a few fuzzy metric spaces.

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