Metrization of probabilistic metric spaces. Applications to fixed point theory and Arzela-Ascoli type theorem - Archive ouverte HAL Access content directly
Journal Articles Topology and its Applications Year : 2021

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

(1) , (1)
1
Nazaret Bruno

#### 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.

#### Domains

Mathematics [math] Functional Analysis [math.FA]

### Dates and versions

hal-03075552 , version 1 (16-12-2020)

### Identifiers

• HAL Id : hal-03075552 , version 1

### Cite

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

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

47 View