A note on convergence in fuzzy metric spaces

Document Type : Research Paper

Authors

1 Instituto Universitario de Matematica Pura y Aplicada, Universitat Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

2 Instituto Universitario de Matematica Pura y Aplicada, Universitat Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

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.

Keywords


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