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 |
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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 |
| _version_ | 1797254058212327424 |
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| author | Dirk Langemann Olesia Zavarzina |
| author_facet | Dirk Langemann Olesia Zavarzina |
| author_sort | Dirk Langemann |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T21:43:55Z |
| format | Article |
| id | doaj.art-a2258d6bb8344ab3bdf6159e2a6d79e9 |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-04-24T21:43:55Z |
| publishDate | 2024-03-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-a2258d6bb8344ab3bdf6159e2a6d79e92024-03-21T04:44:03ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872024-03-011010.3389/fams.2024.13870121387012Expand-contract plasticity on the real lineDirk Langemann0Olesia Zavarzina1Institute of Partial Differential Equations, Technische Universität Braunschweig, Braunschweig, GermanyDepartment of Mathematics and Informatics, V.N. Karazin Kharkiv National University, Kharkiv, UkraineThe 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.https://www.frontiersin.org/articles/10.3389/fams.2024.1387012/fullmetric spacenon-expansive mapplastic spaceexpand-contract plasticityBanach space |
| spellingShingle | Dirk Langemann Olesia Zavarzina Expand-contract plasticity on the real line Frontiers in Applied Mathematics and Statistics metric space non-expansive map plastic space expand-contract plasticity Banach space |
| title | Expand-contract plasticity on the real line |
| title_full | Expand-contract plasticity on the real line |
| title_fullStr | Expand-contract plasticity on the real line |
| title_full_unstemmed | Expand-contract plasticity on the real line |
| title_short | Expand-contract plasticity on the real line |
| title_sort | expand contract plasticity on the real line |
| topic | metric space non-expansive map plastic space expand-contract plasticity Banach space |
| url | https://www.frontiersin.org/articles/10.3389/fams.2024.1387012/full |
| work_keys_str_mv | AT dirklangemann expandcontractplasticityontherealline AT olesiazavarzina expandcontractplasticityontherealline |