Real Jacobian conjecture

Let $F:\mathbb{R}^n\to\mathbb{R}^n$ be a polynomial map. Real Jacobian conjecture. If

$$\det F'(x)\ne 0\qquad\text{for every }x\in\mathbb{R}^n,$$

then $F$ is injective. The source explains that this real analogue is false: Pinchuk constructed a counterexample for $n=2$, so the conjecture is refuted.