The Convex Peano Curve Does Exist
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910511503769600 |
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| author | Paszkiewicz, Adam |
| author_facet | Paszkiewicz, Adam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03016 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Convex Peano Curve Does Exist Paszkiewicz, Adam Metric Geometry 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. |
| title | The Convex Peano Curve Does Exist |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2407.03016 |