A Banach-Stone type Theorem for invariant metric groups - Archive ouverte HAL Access content directly
Journal Articles Topology and its Applications Year : 2016

## A Banach-Stone type Theorem for invariant metric groups

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Mohammed Bachir
• Function : Author
• PersonId : 960537

#### 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.

#### Domains

Mathematics [math] Functional Analysis [math.FA]

### Dates and versions

hal-01333611 , version 1 (17-06-2016)

### Identifiers

• HAL Id : hal-01333611 , version 1

### Cite

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

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