3-Schur property for Lipschitz-free spaces over complete metric spaces without isolated points

Determine whether, for every complete metric space without isolated points (as described in the paper’s item (i)), the associated Lipschitz-free space F(M) has the 3-Schur property.

Background

The general question about the 3-Schur property for complete purely 1-unrectifiable spaces is refined by the authors to specific subclasses. One such subclass consists of complete metric spaces without isolated points (not necessarily uniformly discrete). Whether their Lipschitz-free spaces are 3-Schur remains unresolved.

References

In particular, the following special cases remain open.

(i) Assume that $M$ is a complete discrete metric space (i.e., a complete space without isolated points, not necessarily uniformly discrete). Is $(M)$ $3$-Schur?

— Lipschitz-free spaces over uniformly discrete metric spaces are 3-Schur  (2604.01875 - Cúth et al., 2 Apr 2026) in Introduction, Question (special cases remain open), item (i)