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