On Principal Fuzzy Metric Spaces

In this paper, we deal with the notion of fuzzy metric space (X,M,∗), or simply X, due to George and Veeramani. It is well known that such spaces, in general, are not completable also there exist p-Cauchy sequences which Cauchy. We prove if every sequence X Cauchy, then principal, observe converse false, general. Hence, introduce study a stronger concept than called strongly principal. Moreover, weak p-complete p-convergent. principal (or principal), family agrees Cauchy sequences. Among other results related completeness, where M strong respect an integral (positive) t-norm ∗ admits completion.