ON COMPACTNESS AND G-COMPLETENESS IN FUZZY METRIC SPACES
نویسنده
چکیده مقاله:
In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case, for which we present an example of a compact fuzzy metric space that is not complete in Grabiecs sense. On the other hand, Grabiec used a notion of compactness to obtain a fuzzy version of Edelstein s contraction principle. We present here a generalized version of Grabiecs version of the Edelstein xed point theorem and dierent interesting facts on the topology of fuzzy metric spaces.
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عنوان ژورنال
دوره 9 شماره 4
صفحات 151- 158
تاریخ انتشار 2012-10-01
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