Centered Takagi--van der Waerden functions and their Lipschitz derivatives
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909572808048640 |
|---|---|
| author | Maslyuchenko, Oleksandr V. Wójcicki, Ziemowit M. |
| author_facet | Maslyuchenko, Oleksandr V. Wójcicki, Ziemowit M. |
| contents | Using a modification of a generalized Takagi-van der Waerden function on a metric space we prove that for any closed subset of a metric space without isolated points there exists a continuous function such that its big and local Lipschitz derivatives are equal to infinity exactly on this set. Moreover, if given space is hermetic (for example, if it is normed) then the little Lipschitz derivative has the same property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Centered Takagi--van der Waerden functions and their Lipschitz derivatives Maslyuchenko, Oleksandr V. Wójcicki, Ziemowit M. Functional Analysis 46G05 (Primary), 46T20, 26A16, 26A21 (Secondary) Using a modification of a generalized Takagi-van der Waerden function on a metric space we prove that for any closed subset of a metric space without isolated points there exists a continuous function such that its big and local Lipschitz derivatives are equal to infinity exactly on this set. Moreover, if given space is hermetic (for example, if it is normed) then the little Lipschitz derivative has the same property. |
| title | Centered Takagi--van der Waerden functions and their Lipschitz derivatives |
| topic | Functional Analysis 46G05 (Primary), 46T20, 26A16, 26A21 (Secondary) |
| url | https://arxiv.org/abs/2504.06931 |