%0 Journal Article %T Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem %+ Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM) %A Bachir, Mohammed %A Bruno, Nazaret %< avec comité de lecture %@ 0166-8641 %J Topology and its Applications %I Elsevier %V 289 %8 2021 %D 2021 %Z Mathematics [math]/Functional Analysis [math.FA]Journal articles %X This work is devoted to the metrization of probabilistic spaces. More precisely, given such a space $(G,D,\star)$ and provided that the triangle function $\star$ is continuous, we exhibit an explicit and canonical metric $\sigma_D$ on $G$ such that the associated topology is homeomorphic to the so-called strong topology. As applications, we make advantage of this explicit metric to present some fixed point theorems on such probabilistic metric structures and we prove a probabilistic version of the Arzela-Ascoli theorem. %G English %L hal-03075552 %U https://paris1.hal.science/hal-03075552 %~ UNIV-PARIS1 %~ SAMOS %~ INSMI %~ SAMM