I'm trying to determine the conditions on $f : \mathbb{R}^n_{\ge 0} \to \mathbb{R^n}$ under which $\{ x \ge 0  f(x) \le 0 \}$ is pathconnected. We can assume that $f$ is continuous and concave.
Any advice?
I'm trying to determine the conditions on $f : \mathbb{R}^n_{\ge 0} \to \mathbb{R^n}$ under which $\{ x \ge 0  f(x) \le 0 \}$ is pathconnected. We can assume that $f$ is continuous and concave. Any advice? 

