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10-03-2020 | Foundations

Probabilistic norms on the homeomorphisms of a group

Authors: Alireza Pourmoslemi, Massimiliano Ferrara, Bruno Antonio Pansera, Mehdi Salimi

Published in: Soft Computing | Issue 10/2020

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Abstract

In this paper, a probabilistic metric on the set of all auto-homeomorphisms of a group is presented. We show that the defined probabilistic group metric is right invariant and it implies a probabilistic group norm. In addition, by the probabilistic norm admissibility condition, we study the uniform continuity of homeomorphisms, and finally, we prove some theorems about topologically equivalent probabilistic norms.

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Title: Probabilistic norms on the homeomorphisms of a group
Authors: Alireza Pourmoslemi
Massimiliano Ferrara
Bruno Antonio Pansera
Mehdi Salimi
Publication date: 10-03-2020
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 10/2020
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-020-04818-7

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