Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Abstract : We introduce and study the natural notion of probabilistic $1$-Lipschitz maps. We use the space of all probabilistic $1$-Lipschitz maps to give a new method for the construction of probabilistic metric completion (respectively of probabilistic invariant metric group completion). Our construction is of independent interest. We prove that the space of all probabilistic $1$-Lipschitz maps defined on a probabilistic invariant metric group can be endowed with a monoid structure. Next, we explecite the set of all invertible element of this monoid and characterize the probabilistic invariant complete Menger groups by the space of all probabilistic $1$-Lipschitz maps in the sprit of the classical Banach-Stone theorem.
https://hal-paris1.archives-ouvertes.fr/hal-01973212 Contributor : Mohammed BachirConnect in order to contact the contributor Submitted on : Tuesday, January 8, 2019 - 11:06:50 AM Last modification on : Friday, May 6, 2022 - 4:50:07 PM