Abstract
We prove that the topology induced by any (complete) fuzzy metric space (in the sense of George and Veeramani) is (completely) metrizable. We also show that every separable fuzzy metric space admits a precompact fuzzy metric and that a fuzzy metric space is compact if and only if it is precompact and complete. Finally, we generalize, among other classical results, the Niemytzki–Tychonoff theorem to fuzzy metric spaces.
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