## Some theorems in fuzzy metric spaces.(English)Zbl 0870.54007

Summary: We prove the Ascoli-Arzela theorem for fuzzy metric spaces. We also prove that every fuzzy metric space has a basis that is countably locally finite. We use this result to conclude that every fuzzy metric space is metrizable.

### MSC:

 54A40 Fuzzy topology 54E35 Metric spaces, metrizability