If $(X,\leq)$ is any poset and $a,b\!\in\!X$, then we define the interval as $[a,b]_\leq:=\{x\!\in\!X;\;a\!\leq\!x\!\leq\!b\}.$
If $a,b\!\in\!\mathbb{R}^n$, then we define the line segment as $[a,b]_{\mathbb{R}^n}:=\{a\!+\!t(b\!-\!a);\;t\!\in\![0,1]\}.$
A subset $A\!\subseteq\!X$ is called convex when $\forall a,a'\!\in\!A\!:[a,a']_\leq\!\subseteq A$.
A subset $A\!\subseteq\!\mathbb{R}^n$ is called convex when $\forall a,a'\!\in\!A\!:[a,a']_{\mathbb{R}^n}\!\subseteq A$.
Question: how can I define a partial ordering $\leq$ on $\mathbb{R}^n$, such that $\forall a,b\!\in\!\mathbb{R}^n\!:[a,b]_\leq=[a,b]_{\mathbb{R}^n}$?