The Convex Peano Curve Does Exist
Metric Geometry
2024-07-04 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2407.03016,
title = {The Convex Peano Curve Does Exist},
author = {Adam Paszkiewicz},
journal= {arXiv preprint arXiv:2407.03016},
year = {2024}
}