AUTHOR=Langemann Dirk , Zavarzina Olesia 

TITLE=Expand-contract plasticity on the real line

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=10

YEAR=2024

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1387012

DOI=10.3389/fams.2024.1387012

ISSN=2297-4687

ABSTRACT=<p>The study deals with plastic and non-plastic sub-spaces <italic>A</italic> of the real-line ℝ with the usual Euclidean metric <italic>d</italic>. 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 <italic>A</italic> 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.</p>