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# A Banach-Stone type Theorem for invariant metric groups

1 Equations d'evolution
SAMM - SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
Abstract : Given an invariant metric group $(X,d)$, we prove that the set $Lip^1_+(X)$ of all nonnegative and $1$-Lipschitz maps on $(X,d)$ endowed with the inf-convolution structure is a monoid which completely determine the group completion of $(X,d)$. This gives a Banach-Stone type theorem for the inf-convolution structure in the group framework.
Keywords :
Document type :
Journal articles

https://hal-paris1.archives-ouvertes.fr/hal-01333611
Contributor : Mohammed Bachir Connect in order to contact the contributor
Submitted on : Friday, June 17, 2016 - 7:16:48 PM
Last modification on : Friday, May 6, 2022 - 4:50:07 PM

### Identifiers

• HAL Id : hal-01333611, version 1

### Citation

Mohammed Bachir. A Banach-Stone type Theorem for invariant metric groups. Topology and its Applications, Elsevier, 2016. ⟨hal-01333611⟩

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