  We ask for a given system of polynomials f_1,...,f_n and f over the complex
numbers when there exist continuous functions q_1,...,q_n such that q_1
f_1+...+q_n f_n = f. This condition defines the continuous closure of an ideal.
We give inclusion criteria and exclusion results for this closure in terms of
the algebraically defined axes closure. Conjecturally, continuous and axes
closure are the same, and we prove this in the monomial case.
