Expand-contract plasticity on the real line - Langemann, Dirk; Zavarzina, Olesia (Frontiers in Applied Mathematics and Statistics, 2024)
The paper deals with plastic and non-plastic sub-spaces A of the real line 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.