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Schweizer, Sklar and Thorp proved in 1960 that a Menger space $(G,D,T)$ undera continuous $t$-norm $T$, induce a natural topology $\tau$ wich is metrizable.We extend this result to any probabilistic metric space $(G,D,\star)$ providedthat the triangle function $\star$ is continuous. We prove in this case, thatthe topological space $(G,\tau)$ is uniformly homeomorphic to a (deterministic)metric space $(G,\sigma_D)$ for some canonical metric $\sigma_D$ on $G$. Asapplications, we extend the fixed point theorem of Hicks to probabilisticmetric spaces which are not necessarily Menger spaces and we prove aprobabilistic Arzela-Ascoli type theorem.

Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem