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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
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