ON COMPACTNESS AND G-COMPLETENESS IN FUZZY METRIC SPACES

Document Type : Research Paper

Author

Instituto Universitario de Matematica Pura y Aplicada, Universidad Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

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 xed point theorem and di
erent interesting facts on
the topology of fuzzy metric spaces.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 9, Issue 4 - Serial Number 4
September and October 2012
Pages 151-158

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