论文标题
你能画什么？
What can you draw?
论文作者
论文摘要
我们解决了可以用铅笔和橡皮擦绘制哪种平面集的问题。铅笔绘制了飞机上的任何黑色开放单元磁盘的联合$ \ mathbb {r}^2 $。橡皮擦会产生任何白色开放单元磁盘的结合。您可以根据需要切换工具多次。我们的主要结果是，可绘制性不能以局部障碍物为特征：有限的集合可以在本地绘制，而不可绘制。我们还表明，如果使用封闭的单元磁盘定义了可绘制的集合，那么与涉及开放单元磁盘的定义相比，可绘制集合集合的基数严格更大。
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.
