Continuous approximate roots of polynomial equations via shape theory
Abstract
We study continuous approximate solutions to polynomial equations over the ring $C(X)$ of continuous complex-valued functions over a compact Hausdorff space $X$. We show that when $X$ is one-dimensional, the existence of such approximate solutions is governed by the behaviour of maps from the fundamental pro-group of $X$ into braid groups.
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Polynomial and algebraic computation
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Topology and its Applications
- Publisher
- Elsevier BV
- Volume
- 390
- Pages
- 109894–109894
- Publication date
- 25 June 2026
- Language
- EN