Plastic metric spaces and groups
General Topology
2026-01-05 v2 Functional Analysis
Group Theory
Abstract
A metric space is plastic if all its non-expansive bijections are isometries. We prove three main results: (1) every countable dense subspace of a normed space is not plastic, (2) every -crowded separable metric space contains a plastic dense subspace, and (3) every strictly convex separable metric group contains a plastic dense subgroup.
Cite
@article{arxiv.2510.10537,
title = {Plastic metric spaces and groups},
author = {Taras Banakh and Oles Mazurenko and Olesia Zavarzina},
journal= {arXiv preprint arXiv:2510.10537},
year = {2026}
}
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12 pages