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 García-Lirola, Procházka and Rueda Zoca, and by Becerra Guerrero, López-Pérez and Rueda Zoca, related to the structure of Lipschitz-free Banach spaces of metric spaces.

References in corpus (1)

• On the preserved extremal structure of Lipschitz-free spaces

Cited by in corpus (1)

• On strongly norm attaining Lipschitz maps