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arXiv · 2510.01613

Continuous approximate roots of polynomial equations via shape theory

Joshua Lau·Vicente Marin-Marquez
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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.

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Joshua Lau, Vicente Marin-Marquez. 2025-10-02. Continuous approximate roots of polynomial equations via shape theory. https://arxiv.org/abs/2510.01613

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