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Journal Articles Topology and its Applications Year : 2016

A Banach-Stone type Theorem for invariant metric groups

Mohammed Bachir
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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.
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Dates and versions

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

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  • HAL Id : hal-01333611 , version 1

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