On the completion of fuzzy metric spaces (Q835244)

The main result is the following: Suppose that \((x,d,L,R)\) is a fuzzy metric space. Suppose that \(\{\lambda_0(x_n,y_n) \}^\infty_{n=1}\) and \(\{\rho_0(x_n,y_n)\}^\infty_{n=1}\) are left equicontinuous, whenever \(\{x_n\}\) and \(\{y_n\}\) are Cauchy sequences. Then \((x,d,L,R)\) has a completion which is uniquely determined up to isometry. Also \((x,d,L,R)\) has a unique completion if and only if \(\{\rho_0(x_n,y_n)\}\) is left equicontinuous on \((0,1]\).