Probabilistic norms on the homeomorphisms of a group. (English) Zbl 1490.22002
Summary: 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.
Keywords:
probabilistic normed groups; probabilistic metric groups; continuity of auto-homeomorphisms; probabilistic norm admissibility condition; equal normsReferences:
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