The space of probabilistic 1-lipschitz maps
Functional Analysis
2018-01-18 v2
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.
Keywords
Cite
@article{arxiv.1801.00581,
title = {The space of probabilistic 1-lipschitz maps},
author = {Mohammed Bachir},
journal= {arXiv preprint arXiv:1801.00581},
year = {2018}
}