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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
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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 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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