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THE SPACE OF PROBABILISTIC 1-LIPSCHITZ MAPS

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Abstract

We introduce and study a natural notion of probabilistic 1-Lipschitz maps. We prove that the space of all probabilistic 1-Lipschitz maps defined on a probabilistic metric space G is also a probabilistic metric space. Moreover, when G is a group, then the space of all prob-abilistic 1-Lipschitz maps defined on G can be endowed with a monoid structure. Then, we caracterize the probabilistic invariant complete Menger groups by the space of all probabilistic 1-Lipschitz maps in the sprit of the classical Banach-Stone theorem.
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Dates and versions

hal-01673497 , version 1 (30-12-2017)
hal-01673497 , version 2 (16-01-2018)

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Mohammed Bachir. THE SPACE OF PROBABILISTIC 1-LIPSCHITZ MAPS. 2018. ⟨hal-01673497v2⟩
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