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.


54A40 Fuzzy topology
54E50 Complete metric spaces
54D65 Separability of topological spaces
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[1] Bachmann, G.; Narici, L., Functional Analysis (1966), Academic Press: Academic Press New York · Zbl 0141.11502
[2] Zi-Ke, Deng, Fuzzy pseudo-metric spaces, J. Math. Anal. Appl., 86, 74-95 (1982) · Zbl 0501.54003
[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)
[8] Munkres, J. R., Topology — A First Course (1991), Prentice-Hall: Prentice-Hall Delhi · 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
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