On completion of fuzzy metric spaces

Authors:
Valentín Gregori;Salvador Romaguera
Affiliations:
Escuela Politécnica Superior de Gandia, Universidad Politécnica de Valencia, 46730 Grau de Gandia, Valencia, Spain;Escuela de Caminos, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Camino de Vera 14, Apartado 22.012, 46071 Valencia, Spain
Venue:
Fuzzy Sets and Systems - Fuzzy intervals
Year:
2002

Citing 4
Cited 14

Fixed points in fuzzy metric spaces

Fuzzy Sets and Systems
On some results in fuzzy metric spaces

Fuzzy Sets and Systems
On some results of analysis for fuzzy metric spaces

Fuzzy Sets and Systems
Some properites of fuzzy metric spaces

Fuzzy Sets and Systems

Completeness of Hutton [0,1]-quasi-uniform spaces

Fuzzy Sets and Systems
A comment on the completion of fuzzy metric spaces

Fuzzy Sets and Systems
On the completion of fuzzy metric spaces

Fuzzy Sets and Systems
A characterization of bicompletable fuzzy quasi-metric spaces

Fuzzy Sets and Systems
Fuzzy uniform structures and continuous t-norms

Fuzzy Sets and Systems
On fuzzy pseudo-metric spaces

Fuzzy Sets and Systems
Fuzzy Lipschitz maps and fixed point theorems in fuzzy metric spaces

Fuzzy Sets and Systems
On a class of completable fuzzy metric spaces

Fuzzy Sets and Systems
Non-Archimedean L-fuzzy normed spaces and stability of functional equations

Computers & Mathematics with Applications
The bicompletion of fuzzy quasi-metric spaces

Fuzzy Sets and Systems
Examples of fuzzy metrics and applications

Fuzzy Sets and Systems
Some questions in fuzzy metric spaces

Fuzzy Sets and Systems
Probabilistic metric spaces as enriched categories

Fuzzy Sets and Systems
Fuzzy quasi-metrics for the Sorgenfrey line

Fuzzy Sets and Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

Completions of fuzzy metric spaces (in the sense of George and Veeramani) are discussed. A complete fuzzy metric space Y is said to be a fuzzy metric completion of a given fuzzy metric space X if X is isometric to a dense subspace of Y. We present an example of a fuzzy metric space that does not admit any fuzzy metric completion. However, we prove that every standard fuzzy metric space has an (up to isometry) unique fuzzy metric completion. We also show that for each fuzzy metric space there is an (up to uniform isomorphism) unique complete fuzzy metric space that contains a dense subspace uniformly isomorphic to it.