I am reading the paper Dual-to-Kernel Learning with Ideals. Here is part of it:
The definition/motivation of genericity in Wikipedia are
A generic point of the topological space $X$ is a point $P$ whose closure is all of $X$, that is, a point that is dense in $X$. The terminology arises from the case of the Zariski topology of algebraic varieties. For example having a generic point is a criterion to be an irreducible set.
I cannot see why this gives the linear independence in Theorem 1 immediately. Any hints? Thanks.