Practice problem

Olympiad Euclidean Geometry

Informally, a topological T is any figure consisting of a central point with three nonempty connected tentacles sticking out, like a "floppy letter T".

Can you cover the real plane, $\mathbb{R}^2$ , using a disjoint set of topological T's?

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[Source: Communicated by Mark Sellke, and separately by David (Ting-Chun) Lin, who heard it from Bjorn Poonen]