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On some results in fuzzy metric spaces. (English) Zbl 0843.54014

Summary: We define a Hausdorff topology on a fuzzy metric space introduced by I. Kramosil and J. Michálek [Kybernetika 11, 336-344 (1975; Zbl 0319.54002)]and prove some known results of metric spaces including Baire’s theorem for fuzzy metric spaces.

MSC:

54A40 Fuzzy topology
54E35 Metric spaces, metrizability

Citations:

Zbl 0319.54002
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References:

[1] Zi-ke, Deng, Fuzzy pseudo metric spaces, J. Math. Anal. Appl., 86, 74-95 (1982) · Zbl 0501.54003
[2] Erceg, M. A., Metric spaces in fuzzy set theory, J. Math. Anal. Appl., 69, 205-230 (1979) · Zbl 0409.54007
[3] Kaleva, O.; Seikkala, S., On fuzzy metric spaces, Fuzzy Sets and Systems, 12, 215-229 (1984) · Zbl 0558.54003
[4] Kramosil, O.; Michalek, J., Fuzzy metric and statistical metric spaces, Kybernetica, 11, 326-334 (1975)
[5] Limaye, B. V., Functional Analysis (1981), Wiley Eastern Ltd: Wiley Eastern Ltd New Delhi, India
[6] Grabiec, Mariusz, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27, 385-389 (1988) · Zbl 0664.54032
[7] Schweizer, B.; Sklar, A., Statistical metric spaces, Pacific J. Math., 10, 314-334 (1960) · Zbl 0091.29801
[8] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606
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