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