Continuous approximate roots of polynomial equations via shape theory
Joshua Lau, Vicente Marin-Marquez
公開日: 2025/10/2
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.