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On some results of analysis for fuzzy metric spaces. (English) Zbl 0917.54010
Summary: A necessary and sufficient condition for a fuzzy metric space to be complete is given. The authors prove that a subspace of a separable fuzzy metric space is separable and every separable fuzzy metric space is second countable. A uniform limit theorem is generalized to fuzzy metric spaces.

##### MSC:
 54A40 Fuzzy topology 54E50 Complete metric spaces 54D65 Separability (general topology)
##### Keywords:
fuzzy metric space
Full Text:
##### References:
 [1] Bachmann, G.; Narici, L.: Functional analysis. (1966) · Zbl 0141.11502 [2] Zi-Ke, Deng: Fuzzy pseudo-metric spaces. J. math. Anal. appl. 86, 74-95 (1982) [3] Erceg, M. A.: Metric spaces in fuzzy set theory. J. math. Anal. appl. 69, 205-230 (1979) · Zbl 0409.54007 [4] George, A.; Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy sets and systems 64, 395-399 (1994) · Zbl 0843.54014 [5] Grabiec, M.: Fixed points in fuzzy metric spaces. Fuzzy sets and systems 27, 385-389 (1989) · Zbl 0664.54032 [6] Kaleva, O.; Seikkala, S.: On fuzzy metric spaces. Fuzzy sets and systems 12, 215-229 (1984) · Zbl 0558.54003 [7] Kramosil, O.; Michalek, J.: Fuzzy metric and statistical metric spaces. Kybernetica 11, 326-334 (1975) · Zbl 0319.54002 [8] Munkres, J. R.: Topology -- A first course. (1991) · Zbl 0306.54001 [9] Schweizer, B.; Sklar, A.: Statistical metric spaces. Pacific J. Maths 10, 314-334 (1960) · Zbl 0091.29801 [10] Zadeh, L. A.: Fuzzy sets. Inform. and control 8, 338-353 (1965) · Zbl 0139.24606