Coarse structures and fuzzy metrics. (English) Zbl 1224.54023
Summary: It is known that every fuzzy metric on a set generates a uniform structure on this set. The aim of this note is to show that every fuzzy metric on a set generates a coarse structure on this set. In the case of fuzzy non-Archimedean metric spaces, the obtained coarse space turns out to be asymptotically zero-dimensional in the sense of Gromov.
MSC:
54A40 | Fuzzy topology |
54E35 | Metric spaces, metrizability |
54E15 | Uniform structures and generalizations |