A note on convergence in fuzzy metric spaces

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,\ast) is a fuzzy metric on X where N_M(x,y)=\bigwedge\{M(x,y,t):t>۰\} then it is proved that the topologies deduced from M and N_M coincide if and only if M is an s-fuzzy metric.

Keywords:

Fuzzy metric space , principal fuzzy metric , p-convergence