Continuous solutions to algebraic forcing equations

2006/08/24 by Holger Brenner, Brenner, Holger · 1 citation
Computer Science · Mathematics · #12D10 #13A15 #13B22 #26C10 #54C05 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #General Topology (math.GN) #Polynomial and algebraic computation #math.AC #math.GN #msc:12D10 #msc:13A15 #msc:13B22 #msc:26C10 #msc:54C05

paper · pdf · doi:10.48550/arxiv.math/0608611

are welcome; one change in references

openalex publication_date 2006/08/24 · arxiv created 2006/08/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We ask for a given system of polynomials f₁,...,f_n and f over the complex numbers when there exist continuous functions q₁,...,q_n such that q₁ f₁+...+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.

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• Grothendieck topologies and ideal closure operations

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