A characterization of p-complete fuzzy metric spaces

Abstract

[EN] George and Veeramani characterized complete fuzzy metric spaces ¿ by means of nested sequences of closed sets of X which have fuzzy diameter zero. According to the concept of p-convergence due to D. Mihet, an appropriate concept of p-Cauchy sequence was given. In this paper we introduce for a concept of p-fuzzy diameter zero, which is according to the concept of p-convergence. Then, we characterize by means of certain nested sequences , which have p-fuzzy diameter zero, those fuzzy metric spaces in which p-Cauchy sequences are convergent (p-convergent), called p-complete spaces (w-p-complete spaces). As a consequence of our results we obtain the well-known characterization of a complete metric space by means of nested sequences of closed sets of (X,d).