# A note on convergence in fuzzy metric spaces

Autores UPV Morillas Gómez Samuel, Miñana Prats Juan José, Gregori Gregori Valentín 2014 Iranian Journal of Fuzzy Systems

## Abstract

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.