Continuous solutions to algebraic forcing equations
Commutative Algebra
2007-05-23 v2 General Topology
Abstract
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.
Cite
@article{arxiv.math/0608611,
title = {Continuous solutions to algebraic forcing equations},
author = {Holger Brenner},
journal= {arXiv preprint arXiv:math/0608611},
year = {2007}
}
Comments
are welcome; one change in references