The Convex Peano Curve Does Exist
| Autor: | Paszkiewicz, Adam |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We refer here to the surprising construction made by Giuseppe Peano in 1890. He gave an example of a continuous function (called now the Peano curve) from the unit interval to the whole unit square. We show here the existence of a more general space-filling curve with additional convexity properties. More precisely: by T ? R2 we denote a convex closed and bounded set and we show that there exists a continuous surjection f : [0; 1] 7! T for which the image of any interval is a convex set. |
| Databáze: | arXiv |
| Externí odkaz: |
|