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

Abstract : 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.
Document type :
Journal articles
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https://hal-paris1.archives-ouvertes.fr/hal-03075552
Contributor : Mohammed Bachir Connect in order to contact the contributor
Submitted on : Wednesday, December 16, 2020 - 1:54:00 PM
Last modification on : Friday, May 6, 2022 - 4:50:07 PM

### Identifiers

• HAL Id : hal-03075552, version 1

### Citation

Mohammed Bachir, Nazaret Bruno. Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem. Topology and its Applications, Elsevier, 2021, 289. ⟨hal-03075552⟩

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