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Typo fixing
Daniele Tampieri
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Functions of $\mathbb{R}^d$ preserving convexity of sets

Consider a function $f : \mathbb{R}^d \to \mathbb{R}^d$, with $d\geq 2$, such that:

  • $f$ is injective,
  • For any convex set $A$ of $\mathbb{R}^d$, $f(A)$ is also convex.

What can we say about $f$ ? In particular, is $f$ necessarily affine ? I tend to think yes, but I can't prove it.

Pohoua
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