Zeroes of polynomials on ∞

Consider a polynomial P on complex ∞ space.We prove that if P vanishes at zero, then it also vanishes on a non-separable subspace. For a polynomial on real ∞ space, we prove that if P vanishes on a copy of c0 then it necessarily vanishes on a non-separable subspace. © 2006 Elsevier Inc. All rights reserved