Closedness of finitely generated cones
= Closedness of finitely generated cones
A <finitely generated cone> is a <closed convex cone>. For a convergent sequence of represented vectors, use linearly independent active generators and pass to a subsequence with the same active set. Its coefficients converge through a fixed left inverse and retain nonnegativity. General linear images of closed cones need not be closed; finiteness of the generators supplies the missing argument.