Plastic metric spaces and groups

Taras Banakh; Oles Mazurenko; Olesia Zavarzina

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arXiv · 2510.10537

Plastic metric spaces and groups

Taras Banakh·Oles Mazurenko·Olesia Zavarzina

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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 $k$-crowded separable metric space contains a plastic dense subspace, and (3) every strictly convex separable metric group contains a plastic dense subgroup.

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Taras Banakh, Oles Mazurenko, Olesia Zavarzina. 2025-10-12. Plastic metric spaces and groups. https://arxiv.org/abs/2510.10537

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