Complete metric spaces with property (Z) are length metric spaces
Abstract
We prove that every complete metric space with property (Z) is a length space. These answers questions posed by Garc\'ia-Lirola, Proch\'azka and Rueda Zoca, and by Becerra Guerrero, L\'opez-P\'erez and Rueda Zoca, related to the structure of Lipschitz-free Banach spaces of metric spaces.
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