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Some properties of fuzzy metric spaces

✍ Scribed by Valentı́n Gregori; Salvador Romaguera

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
87 KB
Volume
115
Category
Article
ISSN
0165-0114

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✦ Synopsis

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-Tychono theorem to fuzzy metric spaces.

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