Answering an open question in fuzzy metric spaces

Abstract

This paper answers affirmatively Problem 32 posted in \cite{GMM2012}, proving that, for every stationary fuzzy metric space $(X, M, *)$, the function $M_y(x):=M(x,y)$ defined therein is $\mathbb{R}$-uniformly continuous for all $y\in X$, and furthermore proves that the function $M$ is $\mathbb{R}$-uniformly continuous.