Continuous Solutions to Algebraic Forcing Equations
نویسنده
چکیده
We ask for a given system of polynomials f1, . . . , fn and f over the complex numbers C when there exist continuous functions q1, . . . , qn such that q1f1 + . . . + qnfn = 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. Mathematical Subject Classification (2000): 13A15; 54C05; 12D10; 13B22; 26C10.
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