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Paper Information

Journal:   IRANIAN JOURNAL OF FUZZY SYSTEMS   2012 , Volume 9 , Number 4; Page(s) 151 To 158.
 
Paper: 

ON COMPACTNESS AND G-COMPLETENESS IN FUZZY METRIC SPACES

 
 
Author(s):  TIRADO P.*
 
* 
 
Abstract: 

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 fixed point theorem and different interesting facts on the topology of fuzzy metric spaces.

 
Keyword(s): FUZZY METRIC SPACE, CAUCHY SEQUENCE, G-COMPLETENESS, COMPACTNESS, FIXED POINT THEOREM
 
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