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arXiv · 2311.06150

Expand-contract plasticity on the real line

Dirk Langemann·Olesia Zavarzina
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Abstract

The article deals with plastic and non-plastic sub-spaces $A$ of the real line ${\mathbb{R}}$ with the usual Euclidean metric $d$. It investigates non-expansive bijections, proves properties of such maps and demonstrates their relevance by hands of examples. Finally, it is shown that the plasticity property of a sub-space $A$ contains at least two complementary questions, a purely geometric and a topological one. Both contribute essential aspects to the plasticity property and get more critical in higher dimensions and more abstract metric spaces.

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Dirk Langemann, Olesia Zavarzina. 2023-11-10. Expand-contract plasticity on the real line. https://arxiv.org/abs/2311.06150

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