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...

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Bibliographic Details
Published inFrontiers in applied mathematics and statistics Vol. 10
Main Authors Langemann, Dirk, Zavarzina, Olesia
Format Journal Article
LanguageEnglish
Published Frontiers Media S.A 21.03.2024
Subjects
Banach space
expand-contract plasticity
metric space
non-expansive map
plastic space
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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.
ISSN:2297-4687
2297-4687
DOI:10.3389/fams.2024.1387012