Is it possible to construct a metric in $\mathbb{R}^n $ s.t. it does not induce CONVEX balls? I'm studying point set topology and looking for a counterexample of "Balls are convex". 
We say set $K \subset \mathbb{R}^n $ is convex if $\forall x, y\in K$ implies $\lambda x + \left(1-\lambda y\right)\in K, \forall \lambda \in \mathbb{R}$. 
A counterexample has been found in $\mathbb{Q}$ (where the definition of convex has been specialized to "$\lambda\in\mathbb{Q}$") by using p-adic metric. E.g. consider ball $B_{\text{2-adic}}\left(0, 1\right)$. 

In $\mathbb R^2 $ define $d((x_1,y_1),(x_2,y_2))=\sqrt{|x_1-x_2}+\sqrt{|y_1-y_2|}$.
