Erdős Problem #846

Let $A\subset \mathbb{R}^2$ be an infinite set for which there exists some $\epsilon>0$ such that in any subset of $A$ of size $n$ there are always at least $\epsilon n$ with no three on a line.

Is it true that $A$ is the union of a finite number of sets where no three are on a line?

#846: [Er92b]

geometry

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A problem of Erdős, Nešetřil, and Rödl.

See also [774] and [847].

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