## Chebyshev system

it has been a while I was not post in this forum

I need a little help with this one

First, let me defined the chebyshev system.

A linearly independent set of continuous functions $\{u_0(x),u_1(x),\cdots, u_N(x)\}$ defined on $[a,b]$ is a Chebyshev system if for any $a\leq x_0 and $y_0,\cdots,y_N \in \mathbb{R}$, there is a unique linear combination $u(x)=\sum_{j=0}^N{a_ju_j(x)}$ satisfying $u(x_i)=y_i$ for $i=0,\cdots,N$

in $\mathbb{R}$, the set of $N$ continuous functions consisting of the powers of $x$ form a chebyshev system.

my question is why there is no Chebyshev system in $\mathbb{R}^s$ for $s \geq 2$ ?