Let $(\mathbb R^2, \|\cdot\|)$ be two dimensional normed space and $S=\{x\in\mathbb R^2 : \|x\|=1\}$ the unit sphere of $(\mathbb R^2, \|\cdot\|)$. Since $S$ bounded and closed in $\mathbb R^2$ then it is compact. Does $S$ homeomorphic to the segment $[0,1]$ with usual topolgy? And if so then how to construct such an homeomorphism?