A note on convergence in fuzzy metric spaces

Abstract

[eng] 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 $N_M(x,y)=\bigwedge\{M(x,y,t):t>0\}$ then it is proved that the topologies deduced from M and N_M coincide if and only if M is an s-fuzzy metric.