On convergence in fuzzy metric spaces

The concept of p-convergence in fuzzy metric spaces, in George and Veeramaniʹs sense, has been recently given by D. Mihet in [D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems 158 (2007) 915–921]. In this note we study some aspects relative to this concept and characterize those fuzzy metric spaces, that we call principal, in which the family of p-convergent sequences agrees with the family of convergent sequences. Also a non-completable fuzzy metric space, which is not principal, is given.