Unisolvent point set

In approximation theory, a finite collection of points X ⊂ R n is often called unisolvent for a space W if any element w ∈ W is uniquely determined by its values on X .
X is unisolvent for Π n m (polynomials in n variables of degree at most m) if there exists a unique polynomial in Π n m 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 Π k .