English

Complete metric spaces with property (Z) are length metric spaces

Functional Analysis 2018-08-03 v1 General Topology

Abstract

We prove that every complete metric space with property (Z) is a length space. These answers questions posed by Garc\'{i}a-Lirola, Proch\'{a}zka and Rueda Zoca, and by Becerra Guerrero, L\'{o}pez-P\'{e}rez and Rueda Zoca, related to the structure of Lipschitz-free Banach spaces of metric spaces.

Keywords

Cite

@article{arxiv.1808.00715,
  title  = {Complete metric spaces with property (Z) are length metric spaces},
  author = {Antonio Avilés and Gonzalo Martínez-Cervantes},
  journal= {arXiv preprint arXiv:1808.00715},
  year   = {2018}
}