Year: 2020
Type: preprint
Abstract: We address the problem of which planar sets can be drawn with a pencil and eraser. The pencil draws any union of black open unit disks in the plane $\mathbb{R}^2$. The eraser produces any union of white open unit disks. You may switch tools as many times as desired. Our main result is that drawability cannot be characterized by local obstructions: A bounded set can be locally drawable, while not being drawable. We also show that if drawable sets are defined using closed unit disks the cardinality of the collection of drawable sets is strictly larger compared with the definition involving open unit disks.
Source: arXiv (Cornell University)
Authors: Frick, Florian, Peng, Fei
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4295184659