A note on convergence in fuzzy metric spaces

Abstract

[EN] The sequential p-convergence in a fuzzy metric space, in the sense of George and Veeramani, was introduced by D. Mihet as a weaker concept than convergence. Here we introduce a stronger concept called s-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are s-convergent. In such a case M is called an s-fuzzy metric. If (N-M.,*) is a fuzzy metric on X where N-M(x, y) = Lambda{M(x, y, t) : t>0} then it is proved that the topologies deduced from M and N-M coincide if and only if M is an s-fuzzy metric.