  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.
