Expand-contract plasticity on the real line
The study 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-...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Frontiers Media S.A.
2024-03-01
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Series: | Frontiers in Applied Mathematics and Statistics |
Subjects: | |
Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2024.1387012/full |
Summary: | The study 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. |
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ISSN: | 2297-4687 |