Unisolvent point set

In approximation theory, a finite collection of points X in R^n is said to be unisolvent for a space W if any element w of W is uniquely determined by its values on X.
i.e. X is unisolvent for W = $\Pi _{n}^{m}$ if there exists a unique polynomial in W of lowest possible degree which interpolates the data implied by 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 $\Pi ^{k}$.