Characterizing completable fuzzy metric spaces

doi:10.1016/S0165-0114(03)00161-1

Fuzzy Sets and Systems

Volume 144, Issue 3, 16 June 2004, Pages 411-420

https://doi.org/10.1016/S0165-0114(03)00161-1 Get rights and content

Abstract

Recently we showed the existence of a fuzzy metric space, in the sense of George and Veeramani, which is not completable (Fuzzy Sets and Systems 130 (2002) 399). Here we present an internal characterization of those fuzzy metric spaces that are completable. Some applications are derived and some illustrative examples are given.

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Citation Excerpt :
[10] The class of stationary fuzzy metric spaces was introduced in [15] when the authors were studying completions of fuzzy metric spaces. We extend this definition as follows.
We present a McShane-Whitney extension theorem for real-valued fuzzy Lipschitz maps defined between fuzzy metric spaces. Motivated by the potential applications of the obtained results, we generalize the mathematical theory of extensions of Lipschitz maps to the fuzzy context. We develop the problem in its full generality, explaining the similarities and differences with the classical case of extensions on metric spaces.

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^☆: The authors acknowledge the support of Spanish Ministry of Science and Technology, “Plan Nacional de I+D+I”, and FEDER, under Grant BFM2003-02302. The first listed author also acknowledges the support of Generalitat Valenciana, under Grant CTIDIB/2002/59.

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Characterizing completable fuzzy metric spaces☆

Abstract

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

General Topology