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
Probabilistic norms on the homeomorphisms of a group / Ferrara, Massimiliano; Salimi, Mehdi; Pourmoslemi, Alireza; Pansera, Bruno Antonio. - In: SOFT COMPUTING. - ISSN 1432-7643. - 24:(2020), pp. 7021-7028. [10.1007/s00500-020-04818-7]
Probabilistic norms on the homeomorphisms of a group
Massimiliano FerraraValidation
;Bruno Antonio PanseraFormal Analysis
2020-01-01
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| File | Dimensione | Formato | |
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