Unisolvent point set

In approximation theory, a finite collection of points $$X \subset R^n$$ is often called unisolvent for a space $$W$$ if any element $$w \in W$$ is uniquely determined by its values on $$X$$.

$$X$$ is unisolvent for $$\Pi^m_n$$ (polynomials in n variables of degree at most m) if there exists a unique polynomial in $$\Pi^m_n$$ of lowest possible degree which interpolates the data $$X$$.

Simple examples in $$R$$ would be the fact that two distinct points determine a line, three points determine a parabola, etc. It is clear that over $$R$$, any collection of k + 1 distinct points will uniquely determine a polynomial of lowest possible degree in $$\Pi^k$$.