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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 {\it I. Kramosil} and {\it 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.

54A40Fuzzy topology
54E35Metric spaces, metrizability
Full Text: DOI
[1] Zi-Ke, Deng: Fuzzy pseudo metric spaces. J. math. Anal. appl. 86, 74-95 (1982)
[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) · Zbl 0319.54002
[5] Limaye, B. V.: Functional analysis. (1981) · Zbl 0459.46007
[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