Author/Authors :
Valentin Gregori، Valentin Gregori نويسنده Instituto Universitario de Matematica Pura y Aplicada, Universitat Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain Valentin Gregori, Valentin Gregori , Juan-Jose Minana، Juan-Jose Minana نويسنده Instituto Universitario de Matematica Pura y Aplicada, Universitat Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain Juan-Jose Minana, Juan-Jose Minana , Samuel Morillas، Samuel Morillas نويسنده Instituto Universitario de Matematica Pura y Aplicada, Universitat Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain Samuel Morillas, Samuel Morillas
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.
